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THERMODYNAMIC FORMALISM FOR AMENABLE GROUPS AND COUNTABLE STATE SPACES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-03-15 Elmer R. Beltrán, Rodrigo Bissacot, Luísa Borsato, Raimundo Briceño
Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties, such as an infimum rule. Next, we extend the definitions of different notions of Gibbs measures and prove their existence and equivalence, given some regularity and
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AN EFFECTIVE UPPER BOUND FOR ANTI-CANONICAL VOLUMES OF SINGULAR FANO THREEFOLDS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-03-08 Chen Jiang, Yu Zou
For a real number $0<\epsilon <1/3$ , we show that the anti-canonical volume of an $\epsilon $ -klt Fano $3$ -fold is at most $3,200/\epsilon ^4$ , and the order $O(1/\epsilon ^4)$ is sharp.
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ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-03-04 Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu
We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between Salié sums and to a new equidistribution estimate for the set of modular roots of primes.
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PERFECTING GROUP SCHEMES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-02-16 Kevin Coulembier, Geordie Williamson
We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups and obtains a bijection with the set of classifying spaces of compact connected Lie groups topologically localised away from the characteristic. We also study the representations
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LIMIT SETS OF UNFOLDING PATHS IN OUTER SPACE J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-02-15 Mladen Bestvina, Radhika Gupta, Jing Tao
We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational ${\mathbb R}$ -tree T. We also show that T admits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely
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TRILINEAR FOURIER MULTIPLIERS ON HARDY SPACES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-02-15 Jin Bong Lee, Bae Jun Park
In this paper, we obtain the $H^{p_1}\times H^{p_2}\times H^{p_3}\to H^p$ boundedness for trilinear Fourier multiplier operators, which is a trilinear analogue of the multiplier theorem of Calderón and Torchinsky [4]. Our result improves the trilinear estimate in [22] by additionally assuming an appropriate vanishing moment condition, which is natural in the boundedness into the Hardy space $H^p$ for
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CHARACTERIZATION OF THE REDUCED PERIPHERAL SYSTEM OF LINKS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-02-01 Benjamin Audoux, Jean-Baptiste Meilhan
The reduced peripheral system was introduced by Milnor [18] in the 1950s for the study of links up to link-homotopy, that is, up to homotopies leaving distinct components disjoint; this invariant, however, fails to classify links up to link-homotopy for links of four or more components. The purpose of this paper is to show that the topological information which is detected by Milnor’s reduced peripheral
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GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-01-05 Gabriel Araújo, Igor A. Ferra, Luis F. Ragognette
We present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on $T \times G$ , where T is a compact Riemannian manifold and G is a compact Lie group. These conditions involve the global hypoellipticity of a system of vector fields on G and are weaker than Hörmander’s condition, while generalizing the well known Diophantine conditions on the torus
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A CATEGORICAL APPROACH TO THE BAUM–CONNES CONJECTURE FOR ÉTALE GROUPOIDS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-01-02 Christian Bönicke, Valerio Proietti
We consider the equivariant Kasparov category associated to an étale groupoid, and by leveraging its triangulated structure we study its localization at the ‘weakly contractible’ objects, extending previous work by R. Meyer and R. Nest. We prove the subcategory of weakly contractible objects is complementary to the localizing subcategory of projective objects, which are defined in terms of ‘compactly
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FORMALLY REGULAR RINGS AND DESCENT OF REGULARITY J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2024-01-02 Javier Majadas, Samuel Alvite, Nerea G. Barral
Valuation rings and perfectoid rings are examples of (usually non-Noetherian) rings that behave in some sense like regular rings. We give and study an extension of the concept of regular local rings to non-Noetherian rings so that it includes valuation and perfectoid rings and it is related to Grothendieck’s definition of formal smoothness as in the Noetherian case. For that, we have to take into account
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RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-12-22 Kieran G. O’Grady
We prove existence and unicity of slope-stable vector bundles on a general polarized hyperkähler (HK) variety of type $K3^{[n]}$ with certain discrete invariants, provided the rank and the first two Chern classes of the vector bundle satisfy certain equalities. The latter hypotheses at first glance appear to be quite restrictive, but, in fact, we might have listed almost all slope-stable rigid projectively
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THE CERESA CLASS: TROPICAL, TOPOLOGICAL AND ALGEBRAIC J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-12-21 Daniel Corey, Jordan Ellenberg, Wanlin Li
The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve with a marked point, which is trivial when the curve is hyperelliptic with a marked Weierstrass point. The image of the Ceresa cycle under a certain cycle class map provides a class in étale cohomology called the Ceresa class. Describing the Ceresa class explicitly for nonhyperelliptic curves is in general not easy. We present
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COUNTING DISCRETE, LEVEL-, QUATERNIONIC AUTOMORPHIC REPRESENTATIONS ON J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-12-13 Rahul Dalal
Quaternionic automorphic representations are one attempt to generalize to other groups the special place holomorphic modular forms have among automorphic representations of $\mathrm {GL}_2$ . Here, we use ‘hyperendoscopy’ techniques to develop a general trace formula and understand them on an arbitrary group. Then we specialize this general formula to study quaternionic automorphic representations
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GALOIS REPRESENTATIONS FOR EVEN GENERAL SPECIAL ORTHOGONAL GROUPS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-12-13 Arno Kret, Sug Woo Shin
We prove the existence of $\mathrm {GSpin}_{2n}$ -valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of ${\mathrm {GSO}}_{2n}$ under the local hypotheses that there is a Steinberg component and that the archimedean parameters are regular for the standard representation. This is based on the cohomology of Shimura varieties of
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ON LARGE EXTERNALLY DEFINABLE SETS IN NIP J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-12-04 Martin Bays, Omer Ben-Neria, Itay Kaplan, Pierre Simon
We study cofinal systems of finite subsets of $\omega _1$ . We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: In an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals.
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ON RESIDUES AND CONJUGACIES FOR GERMS OF 1-D PARABOLIC DIFFEOMORPHISMS IN FINITE REGULARITY J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-12-01 Hélène Eynard-Bontemps, Andrés Navas
We study conjugacy classes of germs of nonflat diffeomorphisms of the real line fixing the origin. Based on the work of Takens and Yoccoz, we establish results that are sharp in terms of differentiability classes and order of tangency to the identity. The core of all of this lies in the invariance of residues under low-regular conjugacies. This may be seen as an extension of the fact (also proved in
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A -TYPE CONDITION BEYOND THE KÄHLER REALM J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-28 Jonas Stelzig, Scott O. Wilson
This paper introduces a generalization of the $dd^c$ -condition for complex manifolds. Like the $dd^c$ -condition, it admits a diverse collection of characterizations, and is hereditary under various geometric constructions. Most notably, it is an open property with respect to small deformations. The condition is satisfied by a wide range of complex manifolds, including all compact complex surfaces
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HIGHER MOMENT FORMULAE AND LIMITING DISTRIBUTIONS OF LATTICE POINTS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-28 Mahbub Alam, Anish Ghosh, Jiyoung Han
We establish higher moment formulae for Siegel transforms on the space of affine unimodular lattices as well as on certain congruence quotients of $\mathrm {SL}_d({\mathbb {R}})$ . As applications, we prove functional central limit theorems for lattice point counting for affine and congruence lattices using the method of moments.
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POLISH SPACES OF BANACH SPACES: COMPLEXITY OF ISOMETRY AND ISOMORPHISM CLASSES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-28 Marek Cúth, Martin Doležal, Michal Doucha, Ondřej Kurka
We study the complexities of isometry and isomorphism classes of separable Banach spaces in the Polish spaces of Banach spaces, recently introduced and investigated by the authors in [14]. We obtain sharp results concerning the most classical separable Banach spaces. We prove that the infinite-dimensional separable Hilbert space is characterized as the unique separable infinite-dimensional Banach space
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ON GROUPS OF UNITS OF SPECIAL AND ONE-RELATOR INVERSE MONOIDS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-21 Robert D. Gray, Nik Ruškuc
We investigate the groups of units of one-relator and special inverse monoids. These are inverse monoids which are defined by presentations, where all the defining relations are of the form $r=1$ . We develop new approaches for finding presentations for the group of units of a special inverse monoid, and apply these methods to give conditions under which the group admits a presentation with the same
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ISOMETRIES AND HERMITIAN OPERATORS ON SPACES OF VECTOR-VALUED LIPSCHITZ MAPS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-14 Shiho Oi
We study hermitian operators and isometries on spaces of vector-valued Lipschitz maps with the sum norm. There are two main theorems in this paper. Firstly, we prove that every hermitian operator on $\operatorname {Lip}(X,E)$ , where E is a complex Banach space, is a generalized composition operator. Secondly, we give a complete description of unital surjective complex linear isometries on $\operatorname
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LELONG NUMBERS OF m-SUBHARMONIC FUNCTIONS ALONG SUBMANIFOLDS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-07 Jianchun Chu, Nicholas McCleerey
We study the possible singularities of an m-subharmonic function $\varphi $ along a complex submanifold V of a compact Kähler manifold, finding a maximal rate of growth for $\varphi $ which depends only on m and k, the codimension of V. When $k < m$ , we show that $\varphi $ has at worst log poles along V, and that the strength of these poles is moreover constant along V. This can be thought of as
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CODIMENSION ONE FOLIATIONS IN POSITIVE CHARACTERISTIC J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-06 Wodson Mendson, Jorge Vitório Pereira
We investigate the geometry of codimension one foliations on smooth projective varieties defined over fields of positive characteristic with an eye toward applications to the structure of codimension one holomorphic foliations on projective manifolds.
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LINEAR GROWTH OF TRANSLATION LENGTHS OF RANDOM ISOMETRIES ON GROMOV HYPERBOLIC SPACES AND TEICHMÜLLER SPACES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-11-06 Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition, we prove that non-elementary random walks exhibit at least linear growth of translation lengths. As a corollary, almost every random walk on mapping class groups eventually becomes pseudo-Anosov, and almost every random
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UNIFORM BOUNDS FOR L-FUNCTIONS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-10-17 Bingrong Huang
In this paper, we prove uniform bounds for $\operatorname {GL}(3)\times \operatorname {GL}(2) \ L$ -functions in the $\operatorname {GL}(2)$ spectral aspect and the t aspect by a delta method. More precisely, let $\phi $ be a Hecke–Maass cusp form for $\operatorname {SL}(3,\mathbb {Z})$ and f a Hecke–Maass cusp form for $\operatorname {SL}(2,\mathbb {Z})$ with the spectral parameter $t_f$ . Then for
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GENERALISED AUTOMORPHIC SHEAVES AND THE PROPORTIONALITY PRINCIPLE OF HIRZEBRUCH-MUMFORD J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-10-10 Fritz Hörmann
We axiomatise the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalised automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic vector bundles with prescribed vanishing and pole orders along strata in the compactification, and their quotients. These include, for instance, sheaves
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OPTIMAL GEVREY STABILITY OF HYDROSTATIC APPROXIMATION FOR THE NAVIER-STOKES EQUATIONS IN A THIN DOMAIN J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-09-06 Chao Wang, Yuxi Wang
In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When we have convex initial data with Gevrey regularity of optimal index $\frac {3}{2}$ in the x variable and Sobolev regularity in the y variable, we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes/Prandtl system. Due to our method in the paper being independent
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ODD RANK VECTOR BUNDLES IN ETA-PERIODIC MOTIVIC HOMOTOPY THEORY J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-08-23 Olivier Haution
We observe that, in the eta-periodic motivic stable homotopy category, odd rank vector bundles behave to some extent as if they had a nowhere vanishing section. We discuss some consequences concerning $\operatorname {\mathrm {SL}}^c$ -orientations of motivic ring spectra and the étale classifying spaces of certain algebraic groups. In particular, we compute the classifying spaces of diagonalisable
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p-ADIC L-FUNCTIONS AND RATIONAL POINTS ON CM ELLIPTIC CURVES AT INERT PRIMES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-07-17 Ashay A. Burungale, Shinichi Kobayashi, Kazuto Ota
Let K be an imaginary quadratic field and $p\geq 5$ a rational prime inert in K. For a $\mathbb {Q}$ -curve E with complex multiplication by $\mathcal {O}_K$ and good reduction at p, K. Rubin introduced a p-adic L-function $\mathscr {L}_{E}$ which interpolates special values of L-functions of E twisted by anticyclotomic characters of K. In this paper, we prove a formula which links certain values of
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MORAVA K-THEORY AND FILTRATIONS BY POWERS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-07-04 Tobias Barthel, Piotr Pstrągowski
We prove the convergence of the Adams spectral sequence based on Morava K-theory and relate it to the filtration by powers of the maximal ideal in the Lubin–Tate ring through a Miller square. We use the filtration by powers to construct a spectral sequence relating the homology of the K-local sphere to derived functors of completion and express the latter as cohomology of the Morava stabiliser group
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THE DIAGONAL CYCLE EULER SYSTEM FOR J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-06-13 Raúl Alonso, Francesc Castella, Óscar Rivero
We construct an anticyclotomic Euler system for the Rankin–Selberg convolutions of two modular forms, using p-adic families of generalised Gross–Kudla–Schoen diagonal cycles. As applications of this construction, we prove new results on the Bloch–Kato conjecture in analytic ranks zero and one, and a divisibility towards an Iwasawa main conjecture.
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MILNOR K-THEORY, F-ISOCRYSTALS AND SYNTOMIC REGULATORS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-06-08 Masanori Asakura, Kazuaki Miyatani
We introduce a category of filtered F-isocrystals and construct a symbol map from Milnor K-theory to the group of 1-extensions of filtered F-isocrystals. We show that our symbol map is compatible with the syntomic symbol map to the log syntomic cohomology by Kato and Tsuji. These are fundamental materials in our computations of syntomic regulators which we work in other papers.
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REAL TOPOLOGICAL HOCHSCHILD HOMOLOGY OF SCHEMES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-06-07 Jens Hornbostel, Doosung Park
We prove that real topological Hochschild homology $\mathrm {THR}$ for schemes with involution satisfies base change and descent for the ${\mathbb {Z}/2}$ -isovariant étale topology. As an application, we provide computations for the projective line (with and without involution) and the higher-dimensional projective spaces.
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EQUILIBRIUM STATES FOR CENTER ISOMETRIES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-06-02 Pablo D. Carrasco, Federico Rodriguez-Hertz
We develop a geometric method to establish the existence and uniqueness of equilibrium states associated to some Hölder potentials for center isometries (as are regular elements of Anosov actions), in particular, the entropy maximizing measure and the SRB measure. A characterization of equilibrium states in terms of their disintegrations along stable and unstable foliations is also given. Finally,
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DISTRIBUTION OF FROBENIUS ELEMENTS IN FAMILIES OF GALOIS EXTENSIONS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-05-19 Daniel Fiorilli, Florent Jouve
Given a Galois extension $L/K$ of number fields, we describe fine distribution properties of Frobenius elements via invariants from representations of finite Galois groups and ramification theory. We exhibit explicit families of extensions in which we evaluate these invariants and deduce a detailed understanding and a precise description of the possible asymmetries. We establish a general bound on
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INTRINSIC STABILIZER REDUCTION AND GENERALIZED DONALDSON–THOMAS INVARIANTS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-05-02 Michail Savvas
Let $\sigma $ be a stability condition on the bounded derived category $D^b({\mathop{\mathrm {Coh}}\nolimits } W)$ of a Calabi–Yau threefold W and $\mathcal {M}$ a moduli stack parametrizing $\sigma $ -semistable objects of fixed topological type. We define generalized Donaldson–Thomas invariants which act as virtual counts of objects in $\mathcal {M}$ , fully generalizing the approach introduced by
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A HECKE ACTION ON -MODULES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-04-28 Noriyuki Abe
We construct an action of the affine Hecke category on the principal block $\mathrm {Rep}_0(G_1T)$ of $G_1T$ -modules where G is a connected reductive group over an algebraically closed field of characteristic $p> 0$ , T a maximal torus of G and $G_1$ the Frobenius kernel of G. To define it, we define a new category with a Hecke action which is equivalent to the combinatorial category defined by A
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THE QUANTUM ISOMERIC SUPERCATEGORY J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-04-25 Alistair Savage
We introduce the quantum isomeric supercategory and the quantum affine isomeric supercategory. These diagrammatically defined supercategories, which can be viewed as isomeric analogues of the HOMFLYPT skein category and its affinisation, provide powerful categorical tools for studying the representation theory of the quantum isomeric superalgebras (commonly known as quantum queer superalgebras).
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MODEL CATEGORIES AND PRO-p IWAHORI–HECKE MODULES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-04-04 Nicolas Dupré, Jan Kohlhaase
Let G denote a possibly discrete topological group admitting an open subgroup I which is pro-p. If H denotes the corresponding Hecke algebra over a field k of characteristic p, then we study the adjunction between H-modules and k-linear smooth G-representations in terms of various model structures. If H is a Gorenstein ring, we single out a full subcategory of smooth G-representations which is equivalent
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THE EISENSTEIN IDEAL OF WEIGHT k AND RANKS OF HECKE ALGEBRAS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-03-31 Shaunak V. Deo
Let p and $\ell $ be primes such that $p> 3$ and $p \mid \ell -1$ and k be an even integer. We use deformation theory of pseudo-representations to study the completion of the Hecke algebra acting on the space of cuspidal modular forms of weight k and level $\Gamma _0(\ell )$ at the maximal Eisenstein ideal containing p. We give a necessary and sufficient condition for the $\mathbb {Z}_p$ -rank of this
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-CONNECTEDNESS OF MODULI OF VECTOR BUNDLES ON A CURVE J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-03-20 Amit Hogadi, Suraj Yadav
In this note, we prove that the moduli stack of vector bundles on a curve with a fixed determinant is ${\mathbb A}^1$ -connected. We obtain this result by classifying vector bundles on a curve up to ${\mathbb A}^1$ -concordance. Consequently, we classify ${\mathbb P}^n$ -bundles on a curve up to ${\mathbb A}^1$ -weak equivalence, extending a result in [3] of Asok-Morel. We also give an explicit example
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COMPACTNESS AND STRUCTURE OF ZERO-STATES FOR UNORIENTED AVILES–GIGA FUNCTIONALS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-03-10 M. Goldman, B. Merlet, M. Pegon, S. Serfaty
Motivated by some models of pattern formation involving an unoriented director field in the plane, we study a family of unoriented counterparts to the Aviles–Giga functional. We introduce a nonlinear $\operatorname {\mathrm {curl}}$ operator for such unoriented vector fields as well as a family of even entropies which we call ‘trigonometric entropies’. Using these tools, we show two main theorems which
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A CATEGORICAL QUANTUM TOROIDAL ACTION ON THE HILBERT SCHEMES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-03-06 Yu Zhao
We categorify the commutation of Nakajima’s Heisenberg operators $P_{\pm 1}$ and their infinitely many counterparts in the quantum toroidal algebra $U_{q_1,q_2}(\ddot {gl_1})$ acting on the Grothendieck groups of Hilbert schemes from [10, 24, 26, 32]. By combining our result with [26], one obtains a geometric categorical $U_{q_1,q_2}(\ddot {gl_1})$ action on the derived category of Hilbert schemes
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UNIFORM LOCAL CONSTANCY OF ÉTALE COHOMOLOGY OF RIGID ANALYTIC VARIETIES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-03-01 Kazuhiro Ito
We prove some $\ell $ -independence results on local constancy of étale cohomology of rigid analytic varieties. As a result, we show that a closed subscheme of a proper scheme over an algebraically closed complete non-archimedean field has a small open neighbourhood in the analytic topology such that, for every prime number $\ell $ different from the residue characteristic, the closed subscheme and
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GENERALISATIONS OF LODAY’S ASSEMBLY MAPS FOR LAWVERE’S ALGEBRAIC THEORIES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-02-22 Anna Marie Bohmann, Markus Szymik
Loday’s assembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalisation that places both ingredients on the same footing. Building on Elmendorf–Mandell’s multiplicativity results and our earlier work, we show that the K-theory of Lawvere theories is lax monoidal. This result makes it possible to present
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INTEGRAL POINTS ON SINGULAR DEL PEZZO SURFACES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-01-04 Ulrich Derenthal, Florian Wilsch
In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type $\mathbf {A}_1+\mathbf {A}_3$ and prove an analogue of Manin’s conjecture for integral points with respect to its singularities and its lines.
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UNITARY REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS AT ROOTS OF UNITY: COMBINATORIAL CLASSIFICATION AND BGG RESOLUTIONS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2023-01-04 Chris Bowman, Emily Norton, José Simental
We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras, and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in terms of both multipartition combinatorics and as the points in the fundamental alcove under the action of an affine Weyl group. Finally, we cohomologically construct
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BANACH SPACES IN WHICH LARGE SUBSETS OF SPHERES CONCENTRATE J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-12-27 Piotr Koszmider
We construct a nonseparable Banach space $\mathcal {X}$ (actually, of density continuum) such that any uncountable subset $\mathcal {Y}$ of the unit sphere of $\mathcal {X}$ contains uncountably many points distant by less than $1$ (in fact, by less then $1-\varepsilon $ for some $\varepsilon>0$ ). This solves in the negative the central problem of the search for a nonseparable version of Kottman’s
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STRUCTURAL STABILITY OF MEANDERING-HYPERBOLIC GROUP ACTIONS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-12-27 Michael Kapovich, Sungwoon Kim, Jaejeong Lee
In his 1985 paper, Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper, we relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group actions on geodesic metric spaces. This generalization is substantial enough to encompass actions of certain nonhyperbolic groups, such
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BERRY–ESSEEN BOUND AND LOCAL LIMIT THEOREM FOR THE COEFFICIENTS OF PRODUCTS OF RANDOM MATRICES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-12-07 Tien-Cuong Dinh, Lucas Kaufmann, Hao Wu
Let $\mu $ be a probability measure on $\mathrm {GL}_d(\mathbb {R})$ , and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $\mu $ . Under the assumptions that $\mu $ has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we prove a Berry–Esseen bound with the optimal rate $O(1/\sqrt n)$ for the coefficients
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SPECIAL VALUES OF ZETA-FUNCTIONS OF REGULAR SCHEMES J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-12-06 Stephen Lichtenbaum
We formulate a conjecture on the special values of zeta functions of regular arithmetic schemes in terms of Weil-étale cohomology…
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HYPERBOLIC MANIFOLDS THAT FIBRE ALGEBRAICALLY UP TO DIMENSION 8 J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-11-10 Giovanni Italiano, Bruno Martelli, Matteo Migliorini
We construct some cusped finite-volume hyperbolic n-manifolds $M^n$ that fibre algebraically in all the dimensions $5\leq n \leq 8$ . That is, there is a surjective homomorphism $\pi _1(M^n) \to {\mathbb {Z}}$ with finitely generated kernel. The kernel is also finitely presented in the dimensions $n=7, 8$ , and this leads to the first examples of hyperbolic n-manifolds $\widetilde M^n$ whose fundamental
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GOOD REDUCTION AND CYCLIC COVERS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-10-24 Ariyan Javanpeykar, Daniel Loughran, Siddharth Mathur
We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafarevich conjecture for weighted projective surfaces, double covers of abelian varieties and reduce the Shafarevich conjecture for hypersurfaces to the case of hypersurfaces of high dimension. These are special cases of a general
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ON MORPHISMS KILLING WEIGHTS AND STABLE HUREWICZ-TYPE THEOREMS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-10-24 Mikhail V. Bondarko
For a weight structurewon a triangulated category$\underline {C}$we prove that the correspondingweight complexfunctor and some other (weight-exact) functors are ‘conservative up to weight-degenerate objects’; this improves earlier conservativity formulations. In the case$w=w^{sph}$(thesphericalweight structure on$SH$), we deduce the following converse to the stable Hurewicz theorem:$H^{sing}_{i}(M)=\{0\}$for
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PONTRYAGIN DUALITY FOR VARIETIES OVER p-ADIC FIELDS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-09-28 Thomas H. Geisser, Baptiste Morin
We define cohomological complexes of locally compact abelian groups associated with varieties over p-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact motivic cohomology groups.
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THE STABLE LIMIT DAHA AND THE DOUBLE DYCK PATH ALGEBRA J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-09-26 Bogdan Ion, Dongyu Wu
We study the compatibility of the action of the DAHA of type GL with two inverse systems of polynomial rings obtained from the standard Laurent polynomial representations. In both cases, the crucial analysis is that of the compatibility of the action of the Cherednik operators. Each case leads to a representation of a limit structure (the +/– stable limit DAHA) on a space of almost symmetric polynomials
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VARIANTS OF A MULTIPLIER THEOREM OF KISLYAKOV J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-09-01 Andreas Defant, Mieczysław Mastyło, Antonio Pérez-Hernández
We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislyakov and the Kahane–Salem–Zygmund inequality. As a by-product, we show various multiplier theorems for spaces of trigonometric polynomials on the n-dimensional torus $\mathbb {T}^n$ or Boolean cubes $\{-1,1\}^N$. Our more abstract approach based on local Banach space theory has the advantage
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A DERIVED LAGRANGIAN FIBRATION ON THE DERIVED CRITICAL LOCUS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-08-31 Albin Grataloup
We study the symplectic geometry of derived intersections of Lagrangian morphisms. In particular, we show that for a functional $f : X \rightarrow \mathbb {A}_{k}^{1}$, the derived critical locus has a natural Lagrangian fibration $\textbf {Crit}(f) \rightarrow X$. In the case where f is nondegenerate and the strict critical locus is smooth, we show that the Lagrangian fibration on the derived critical
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COHOMOLOGICAL MACKEY 2-FUNCTORS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-08-18 Paul Balmer, Ivo Dell’Ambrogio
We show that the bicategory of finite groupoids and right-free permutation bimodules is a quotient of the bicategory of Mackey 2-motives introduced in [2], obtained by modding out the so-called cohomological relations. This categorifies Yoshida’s theorem for ordinary cohomological Mackey functors and provides a direct connection between Mackey 2-motives and the usual blocks of representation theory
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THE OPTIMAL MALLIAVIN-TYPE REMAINDER FOR BEURLING GENERALIZED INTEGERS J. Inst. Math. Jussieu (IF 0.9) Pub Date : 2022-08-09 Frederik Broucke, Gregory Debruyne, Jasson Vindas
We establish the optimal order of Malliavin-type remainders in the asymptotic density approximation formula for Beurling generalized integers. Given $\alpha \in (0,1]$ and $c>0$ (with $c\leq 1$ if $\alpha =1$), a generalized number system is constructed with Riemann prime counting function $ \Pi (x)= \operatorname {\mathrm {Li}}(x)+ O(x\exp (-c \log ^{\alpha } x ) +\log _{2}x), $ and whose integer