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ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL MODULAR FORMS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-03-03 Siegfried Böcherer; Soumya Das
We prove that if F is a nonzero (possibly noncuspidal) vector-valued Siegel modular form of any degree, then it has infinitely many nonzero Fourier coefficients which are indexed by half-integral matrices having odd, square-free (and thus fundamental) discriminant. The proof uses an induction argument in the setting of vector-valued modular forms. Further, as an application of a variant of our result
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KUMMER COVERINGS AND SPECIALISATION J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-03-01 Martin Olsson
We prove versions of various classical results on specialisation of fundamental groups in the context of log schemes in the sense of Fontaine and Illusie, generalising earlier results of Hoshi, Lepage and Orgogozo. The key technical result relates the category of finite Kummer étale covers of an fs log scheme over a complete Noetherian local ring to the Kummer étale coverings of its reduction.
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THE METRIC PROJECTIONS ONTO CLOSED CONVEX CONES IN A HILBERT SPACE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-02-11 Yanqi Qiu; Zipeng Wang
We study the metric projection onto the closed convex cone in a real Hilbert space $\mathscr {H}$ generated by a sequence $\mathcal {V} = \{v_n\}_{n=0}^\infty $. The first main result of this article provides a sufficient condition under which the closed convex cone generated by $\mathcal {V}$ coincides with the following set: $$ \begin{align*} \mathcal{C}[[\mathcal{V}]]: = \bigg\{\sum_{n=0}^\infty
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CUTOFF AT THE ENTROPIC TIME FOR RANDOM WALKS ON COVERED EXPANDER GRAPHS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-02-09 Charles Bordenave; Hubert Lacoin
It is a fact simple to establish that the mixing time of the simple random walk on a d-regular graph $G_n$ with n vertices is asymptotically bounded from below by $\frac {d }{d-2 } \frac {\log n}{\log (d-1)}$. Such a bound is obtained by comparing the walk on $G_n$ to the walk on d-regular tree $\mathcal{T} _d$. If one can map another transitive graph $\mathcal{G} $ onto $G_n$, then we can improve
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RAISING THE LEVEL OF AUTOMORPHIC REPRESENTATIONS OF OF UNITARY TYPE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-02-09 Christos Anastassiades; Jack A. Thorne
We use the endoscopic classification of automorphic representations of even-dimensional unitary groups to construct level-raising congruences.
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RANDOM REAL BRANCHED COVERINGS OF THE PROJECTIVE LINE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-02-09 Michele Ancona
In this paper, we construct a natural probability measure on the space of real branched coverings from a real projective algebraic curve $(X,c_X)$ to the projective line $(\mathbb{C} \mathbb {P}^1,\textit{conj} )$. We prove that the space of degree d real branched coverings having “many” real branched points (for example, more than $\sqrt {d}^{1+\alpha }$, for any $\alpha>0$) has exponentially small
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INVERSE OF FREQUENTLY HYPERCYCLIC OPERATORS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-02-04 Quentin Menet
We show that there exists an invertible frequently hypercyclic operator on $\ell ^1(\mathbb {N})$ whose inverse is not frequently hypercyclic.
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KODAIRA DIMENSION OF UNIVERSAL HOLOMORPHIC SYMPLECTIC VARIETIES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-02-02 Shouhei Ma
We prove that the Kodaira dimension of the n-fold universal family of lattice-polarised holomorphic symplectic varieties with dominant and generically finite period map stabilises to the moduli number when n is sufficiently large. Then we study the transition of Kodaira dimension explicitly, from negative to nonnegative, for known explicit families of polarised symplectic varieties. In particular,
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IHARA LEMMA AND LEVEL RAISING IN HIGHER DIMENSION J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-25 Pascal Boyer
A key ingredient in the Taylor–Wiles proof of Fermat’s last theorem is the classical Ihara lemma, which is used to raise the modularity property between some congruent Galois representations. In their work on Sato and Tate, Clozel, Harris and Taylor proposed a generalisation of the Ihara lemma in higher dimension for some similitude groups. The main aim of this paper is to prove some new instances
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ON PROJECTIVE MANIFOLDS WITH PSEUDO-EFFECTIVE TANGENT BUNDLE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-25 Genki Hosono; Masataka Iwai; Shin-Ichi Matsumura
In this paper, we develop the theory of singular Hermitian metrics on vector bundles. As an application, we give a structure theorem of a projective manifold X with pseudo-effective tangent bundle; X admits a smooth fibration $X \to Y$ to a flat projective manifold Y such that its general fibre is rationally connected. Moreover, by applying this structure theorem, we classify all the minimal surfaces
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SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-25 Agustin Moreno
I construct infinitely many nondiffeomorphic examples of $5$-dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction results for symplectic cobordisms, for which I give a proof not relying on the polyfold abstract perturbation scheme for Symplectic Field Theory (SFT). These results are part of my PhD thesis [23], and are the first
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THÉORIE DE BRUHAT-TITS POUR LES GROUPES QUASI-RÉDUCTIFS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-25 João Lourenço
Soient K un corps discrètement valué et hensélien, ${\mathcal {O}}$ son anneau d'entiers supposé excellent, $\kappa $ son corps résiduel supposé parfait et G un K-groupe quasi-réductif, c'est-à-dire lisse, affine, connexe et à radical unipotent déployé trivial. On construit l'immeuble de Bruhat-Tits ${\mathcal {I}}(G, K)$ pour $G(K)$ de façon canonique, améliorant les constructions moins canoniques
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BOUNDNESS OF INTERSECTION NUMBERS FOR ACTIONS BY TWO-DIMENSIONAL BIHOLOMORPHISMS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-22 Javier Ribón
We say that a group G of local (maybe formal) biholomorphisms satisfies the uniform intersection property if the intersection multiplicity $(\phi (V), W)$ takes only finitely many values as a function of G for any choice of analytic sets V and W of complementary dimension. In dimension $2$ we show that G satisfies the uniform intersection property if and only if it is finitely determined – that is
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EQUIVALENCE OF ELLIPTICITY AND THE FREDHOLM PROPERTY IN THE WEYL-HÖRMANDER CALCULUS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-20 Stevan Pilipović; Bojan Prangoski
The main result is that the ellipticity and the Fredholm property of a $\Psi $DO acting on Sobolev spaces in the Weyl-Hörmander calculus are equivalent when the Hörmander metric is geodesically temperate and its associated Planck function vanishes at infinity. The proof is essentially related to the following result that we prove for geodesically temperate Hörmander metrics: If $\lambda \mapsto a_{\lambda
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EXTREMAL CASES OF RAPOPORT–ZINK SPACES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-20 Ulrich Görtz; Xuhua He; Michael Rapoport
We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is
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THE COHOMOLOGY OF UNRAMIFIED RAPOPORT–ZINK SPACES OF EL-TYPE AND HARRIS'S CONJECTURE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-14 Alexander Bertoloni Meli
We study the l-adic cohomology of unramified Rapoport–Zink spaces of EL-type. These spaces were used in Harris and Taylor's proof of the local Langlands correspondence for $\mathrm {GL_n}$ and to show local–global compatibilities of the Langlands correspondence. In this paper we consider certain morphisms $\mathrm {Mant}_{b, \mu }$ of Grothendieck groups of representations constructed from the cohomology
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ATIYAH CLASS AND CHERN CHARACTER FOR GLOBAL MATRIX FACTORISATIONS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-08 Bumsig Kim; Alexander Polishchuk
We define the Atiyah class for global matrix factorisations and use it to give a formula for the categorical Chern character and the boundary-bulk map for matrix factorisations, generalising the formula in the local case obtained in [12]. Our approach is based on developing the Lie algebra analogies observed by Kapranov [7] and Markarian [9].
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LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-08 Yaroslav V. Bazaikin; Anton S. Galaev
Following Losik’s approach to Gelfand’s formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for nontriviality in terms of dynamical properties of generators of the holonomy groups are found. The nontriviality for the Reeb foliations is shown; this is in contrast with some classical theorems on
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ON A CERTAIN LOCAL IDENTITY FOR LAPID–MAO'S CONJECTURE AND FORMAL DEGREE CONJECTURE : EVEN UNITARY GROUP CASE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-08 Kazuki Morimoto
Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients of automorphic forms on quasi-split reductive groups and metaplectic groups as an analogue of the Ichino–Ikeda conjecture. They also showed that this conjecture is reduced to a certain local identity in the case of unitary groups. In this article, we study the even unitary-group case. Indeed, we prove this
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RECURSION FOR MASUR-VEECH VOLUMES OF MODULI SPACES OF QUADRATIC DIFFERENTIALS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-08 Maxim Kazarian
We derive a quadratic recursion relation for the linear Hodge integrals of the form $\langle \tau _{2}^{n}\lambda _{k}\rangle $ . These numbers are used in a formula for Masur-Veech volumes of moduli spaces of quadratic differentials discovered by Chen, Möller and Sauvaget. Therefore, our recursion provides an efficient way of computing these volumes.
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VARIATION ON A THEME BY KISELEV AND NAZAROV: HÖLDER ESTIMATES FOR NONLOCAL TRANSPORT-DIFFUSION, ALONG A NON-DIVERGENCE-FREE BMO FIELD J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2021-01-08 Ioann Vasilyev; François Vigneron
We prove uniform Hölder regularity estimates for a transport-diffusion equation with a fractional diffusion operator and a general advection field in of bounded mean oscillation, as long as the order of the diffusion dominates the transport term at small scales; our only requirement is the smallness of the negative part of the divergence in some critical Lebesgue space. In comparison to a celebrated
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EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-12-22 Bart Michels
Given a closed geodesic on a compact arithmetic hyperbolic surface, we show the existence of a sequence of Laplacian eigenfunctions whose integrals along the geodesic exhibit nontrivial growth. Via Waldspurger’s formula we deduce a lower bound for central values of Rankin-Selberg L-functions of Maass forms times theta series associated to real quadratic fields.
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ISOTROPIC MOTIVES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-12-22 Alexander Vishik
In this article we introduce the local versions of the Voevodsky category of motives with $\mathbb{F} _p$-coefficients over a field k, parametrized by finitely generated extensions of k. We introduce the so-called flexible fields, passage to which is conservative on motives. We demonstrate that, over flexible fields, the constructed local motivic categories are much simpler than the global one and
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LOCALIZATION BY -PERIODIC COMPLEXES AND VIRTUAL STRUCTURE SHEAVES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-12-22 Jeongseok Oh; Bhamidi Sreedhar
In [12], Kim and the first author proved a result comparing the virtual fundamental classes of the moduli spaces of $\varepsilon $-stable quasimaps and $\varepsilon $-stable $LG$-quasimaps by studying localized Chern characters for $2$-periodic complexes. In this paper, we study a K-theoretic analogue of the localized Chern character map and show that for a Koszul $2$-periodic complex it coincides
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ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-12-22 Étienne Fouvry; Peter Koymans; Carlo Pagano
We show that for $100\%$ of the odd, square free integers $n> 0$, the $4$-rank of $\text {Cl}(\mathbb{Q} (i, \sqrt {n}))$ is equal to $\omega _3(n) - 1$, where $\omega _3$ is the number of prime divisors of n that are $3$ modulo $4$.
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RECOVERY OF ZEROTH ORDER COEFFICIENTS IN NON-LINEAR WAVE EQUATIONS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-09-18 Ali Feizmohammadi; Lauri Oksanen
This paper is concerned with the resolution of an inverse problem related to the recovery of a function $V$ from the source to solution map of the semi-linear equation $(\Box _{g}+V)u+u^{3}=0$ on a globally hyperbolic Lorentzian manifold $({\mathcal{M}},g)$ . We first study the simpler model problem, where $({\mathcal{M}},g)$ is the Minkowski space, and prove the unique recovery of $V$ through the
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COHERENCE, LOCAL INDICABILITY AND NONPOSITIVE IMMERSIONS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-09-17 Daniel T. Wise
We examine 2-complexes $X$ with the property that for any compact connected $Y$ , and immersion $Y\rightarrow X$ , either $\unicode[STIX]{x1D712}(Y)\leqslant 0$ or $\unicode[STIX]{x1D70B}_{1}Y=1$ . The mapping torus of an endomorphism of a free group has this property. Every irreducible 3-manifold with boundary has a spine with this property. We show that the fundamental group of any 2-complex with
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ALGEBRAIC FIBER SPACES AND CURVATURE OF HIGHER DIRECT IMAGES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-09-03 Bo Berndtsson; Mihai Păun; Xu Wang
Let $p:X\rightarrow Y$ be an algebraic fiber space, and let $L$ be a line bundle on $X$ . In this article, we obtain a curvature formula for the higher direct images of $\unicode[STIX]{x1D6FA}_{X/Y}^{i}\otimes L$ restricted to a suitable Zariski open subset of $X$ . Our results are particularly meaningful if $L$ is semi-negatively curved on $X$ and strictly negative or trivial on smooth fibers of $p$
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GLOBALLY REALIZABLE COMPONENTS OF LOCAL DEFORMATION RINGS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-09-03 Frank Calegari; Matthew Emerton; Toby Gee
Let $n$ be either $2$ or an odd integer greater than $1$ , and fix a prime $p>2(n+1)$ . Under standard ‘adequate image’ assumptions, we show that the set of components of $n$ -dimensional $p$ -adic potentially semistable local Galois deformation rings that are seen by potentially automorphic compatible systems of polarizable Galois representations over some CM field is independent of the particular
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DERIVED NON-ARCHIMEDEAN ANALYTIC HILBERT SPACE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-08-26 Jorge António; Mauro Porta
In this short paper, we combine the representability theorem introduced in [Porta and Yu, Representability theorem in derived analytic geometry, preprint, 2017, arXiv:1704.01683; Porta and Yu, Derived Hom spaces in rigid analytic geometry, preprint, 2018, arXiv:1801.07730] with the theory of derived formal models introduced in [António, $p$ -adic derived formal geometry and derived Raynaud localization
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THE MINIMAL MODULAR FORM ON QUATERNIONIC $E_{8}$ J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-08-20 Aaron Pollack
Suppose that $G$ is a simple reductive group over $\mathbf{Q}$ , with an exceptional Dynkin type and with $G(\mathbf{R})$ quaternionic (in the sense of Gross–Wallach). In a previous paper, we gave an explicit form of the Fourier expansion of modular forms on $G$ along the unipotent radical of the Heisenberg parabolic. In this paper, we give the Fourier expansion of the minimal modular form $\unico
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ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-08-20 Jesús M. F. Castillo; Willian H. G. Corrêa; Valentin Ferenczi; Manuel González
We study the stability of the differential process of Rochberg and Weiss associated with an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces, we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families
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INVARIANT HYPERSURFACES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-08-17 Jason Bell; Rahim Moosa; Adam Topaz
The following theorem, which includes as very special cases results of Jouanolou and Hrushovski on algebraic $D$ -varieties on the one hand, and of Cantat on rational dynamics on the other, is established: Working over a field of characteristic zero, suppose $\unicode[STIX]{x1D719}_{1},\unicode[STIX]{x1D719}_{2}:Z\rightarrow X$ are dominant rational maps from an (possibly nonreduced) irreducible scheme
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PROJECTIVE LOOPS GENERATE RATIONAL LOOP GROUPS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-08-17 Gang Wang; Oliver Goertsches; Erxiao Wang
We generalize Uhlenbeck’s generator theorem of ${\mathcal{L}}^{-}\operatorname{U}_{n}$ to the full rational loop group ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{C}$ and its subgroups ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{R}$ , ${\mathcal{L}}^{-}\operatorname{U}_{p,q}$ : they are all generated by just simple projective loops. Recall that Terng–Uhlenbeck studied the dressing actions of
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LEHN’S FORMULA IN CHOW AND CONJECTURES OF BEAUVILLE AND VOISIN J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-08-03 Davesh Maulik; Andrei Neguţ
The Beauville–Voisin conjecture for a hyperkähler manifold $X$ states that the subring of the Chow ring $A^{\ast }(X)$ generated by divisor classes and Chern characters of the tangent bundle injects into the cohomology ring of $X$ . We prove a weak version of this conjecture when $X$ is the Hilbert scheme of points on a K3 surface for the subring generated by divisor classes and tautological classes
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LAGRANGIAN FIBRATIONS OF HYPERKÄHLER FOURFOLDS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-07-20 Daniel Huybrechts; Chenyang Xu
The base surface $B$ of a Lagrangian fibration of a projective, irreducible symplectic fourfold $X$ is shown to be isomorphic to $\mathbb{P}^{2}$ .
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SHIFTED COISOTROPIC CORRESPONDENCES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-07-03 Rune Haugseng; Valerio Melani; Pavel Safronov
We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks, where the $i$ -morphisms are given by $i$ -fold coisotropic correspondences. Assuming an expected equivalence of different models of higher Morita categories, we prove that all derived Poisson stacks are fully dualizable and so determine framed
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POINCARÉ AND SOBOLEV INEQUALITIES FOR DIFFERENTIAL FORMS IN HEISENBERG GROUPS AND CONTACT MANIFOLDS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-06-29 Annalisa Baldi; Bruno Franchi; Pierre Pansu
In this paper, we prove contact Poincaré and Sobolev inequalities in Heisenberg groups $\mathbb{H}^{n}$ , where the word ‘contact’ is meant to stress that de Rham’s exterior differential is replaced by the exterior differential of the so-called Rumin complex $(E_{0}^{\bullet },d_{c})$ , which recovers the scale invariance under the group dilations associated with the stratification of the Lie algebra
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GLOBAL SUBELLIPTIC ESTIMATES FOR KRAMERS–FOKKER–PLANCK OPERATORS WITH SOME CLASS OF POLYNOMIALS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-06-22 Mona Ben Said
In this article, we study some Kramers–Fokker–Planck operators with a polynomial potential $V(q)$ of degree greater than two having quadratic limiting behaviour. This work provides an accurate global subelliptic estimate for Kramers–Fokker–Planck operators under some conditions imposed on the potential.
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ENHANCED FINITE TRIANGULATED CATEGORIES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-06-18 Fernando Muro
We give a necessary and sufficient condition for the existence of an enhancement of a finite triangulated category. Moreover, we show that enhancements are unique when they exist, up to Morita equivalence.
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GAMES AND HEREDITARY BAIRENESS IN HYPERSPACES AND SPACES OF PROBABILITY MEASURES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-06-15 Mikołaj Krupski
We establish that the existence of a winning strategy in certain topological games, closely related to a strong game of Choquet, played in a topological space $X$ and its hyperspace $K(X)$ of all nonempty compact subsets of $X$ equipped with the Vietoris topology, is equivalent for one of the players. For a separable metrizable space $X$ , we identify a game-theoretic condition equivalent to $K(X)$
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PATCHING AND THE COMPLETED HOMOLOGY OF LOCALLY SYMMETRIC SPACES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-05-27 Toby Gee; James Newton
Under an assumption on the existence of $p$ -adic Galois representations, we carry out Taylor–Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated with $\operatorname{GL}_{n}$ over a number field. We use our construction, and some new results in non-commutative algebra, to show that standard conjectures on completed homology imply ‘big $R=\
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MULTIPLICITY ONE AT FULL CONGRUENCE LEVEL J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-05-15 Daniel Le; Stefano Morra; Benjamin Schraen
Let $F$ be a totally real field in which $p$ is unramified. Let $\overline{r}:G_{F}\rightarrow \text{GL}_{2}(\overline{\mathbf{F}}_{p})$ be a modular Galois representation that satisfies the Taylor–Wiles hypotheses and is tamely ramified and generic at a place $v$ above $p$ . Let $\mathfrak{m}$ be the corresponding Hecke eigensystem. We describe the $\mathfrak{m}$ -torsion in the $\text{mod}\,p$ cohomology
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EXTENSIONS OF VECTOR BUNDLES ON THE FARGUES-FONTAINE CURVE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-05-14 Christopher Birkbeck; Tony Feng; David Hansen; Serin Hong; Qirui Li; Anthony Wang; Lynnelle Ye
We completely classify the possible extensions between semistable vector bundles on the Fargues–Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder–Narasimhan (HN) polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholze’s language of diamonds. This analysis reduces our main
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$\mathbb{A}_{\text{inf}}$ IS INFINITE DIMENSIONAL J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-05-11 Jaclyn Lang; Judith Ludwig
Given a perfect valuation ring $R$ of characteristic $p$ that is complete with respect to a rank- $1$ nondiscrete valuation, we show that the ring $\mathbb{A}_{\inf }$ of Witt vectors of $R$ has infinite Krull dimension.
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SYMBOLIC ANALYTIC SPREAD: UPPER BOUNDS AND APPLICATIONS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-05-07 Hailong Dao; Jonathan Montaño
The symbolic analytic spread of an ideal $I$ is defined in terms of the rate of growth of the minimal number of generators of its symbolic powers. In this article, we find upper bounds for the symbolic analytic spread under certain conditions in terms of other invariants of $I$ . Our methods also work for more general systems of ideals. As applications, we provide bounds for the (local) Kodaira dimension
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UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD $p$ OF WEIGHT 1 J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-04-23 Mladen Dimitrov; Gabor Wiese
The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over $\overline{\mathbb{F}}_{p}$ of parallel weight 1 and level prime to $p$ is unramified above $p$ . This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel
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A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-04-16 Stephen Scully
Let $q$ be an anisotropic quadratic form defined over a general field $F$ . In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization
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RANK TWO TOPOLOGICAL AND INFINITESIMAL EMBEDDED JUMP LOCI OF QUASI-PROJECTIVE MANIFOLDS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-02-15 Stefan Papadima; Alexander I. Suciu
We study the germs at the origin of $G$ -representation varieties and the degree 1 cohomology jump loci of fundamental groups of quasi-projective manifolds. Using the Morgan–Dupont model associated to a convenient compactification of such a manifold, we relate these germs to those of their infinitesimal counterparts, defined in terms of flat connections on those models. When the linear algebraic group
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LIE ALGEBROIDS AS $L_{\infty }$ SPACES J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-02-13 Ryan Grady; Owen Gwilliam
In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) $L_{\infty }$ space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of $L_{\infty }$ spaces. Then we show that for each Lie algebroid
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ON THE GROWTH OF TORSION IN THE COHOMOLOGY OF ARITHMETIC GROUPS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-03-21 A. Ash; P. E. Gunnells; M. McConnell; D. Yasaki
Let $G$ be a semisimple Lie group with associated symmetric space $D$ , and let $\unicode[STIX]{x1D6E4}\subset G$ be a cocompact arithmetic group. Let $\mathscr{L}$ be a lattice inside a $\mathbb{Z}\unicode[STIX]{x1D6E4}$ -module arising from a rational finite-dimensional complex representation of $G$ . Bergeron and Venkatesh recently gave a precise conjecture about the growth of the order of the torsion
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EPSTEIN ZETA-FUNCTIONS, SUBCONVEXITY, AND THE PURITY CONJECTURE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-04-02 Valentin Blomer
Subconvexity bounds on the critical line are proved for general Epstein zeta-functions of $k$ -ary quadratic forms. This is related to sup-norm bounds for unitary Eisenstein series on $\text{GL}(k)$ associated with the maximal parabolic of type $(k-1,1)$ , and the exact sup-norm exponent is determined to be $(k-2)/8$ for $k\geqslant 4$ . In particular, if $k$ is odd, this exponent is not in $\frac{1}{4}\mathbb{Z}$
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A COMPACTNESS THEOREM FOR SURFACES WITH BOUNDED INTEGRAL CURVATURE J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-04-10 Clément Debin
We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$ . As a corollary we obtain a new convergence result for sequences of metrics with conical singularities, where an accumulation of singularities is allowed.
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GENERAL HYPERPLANE SECTIONS OF THREEFOLDS IN POSITIVE CHARACTERISTIC J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2018-04-12 Kenta Sato; Shunsuke Takagi
In this paper, we study the singularities of a general hyperplane section $H$ of a three-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>0$ . We prove that if $X$ has only canonical singularities, then $H$ has only rational double points. We also prove, under the assumption that $p>5$ , that if $X$ has only klt singularities, then so does $H$ .
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JMJ volume 19 Issue 2 Cover and Front matter J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-03-23
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JMJ volume 19 Issue 2 Cover and Back matter J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-03-23
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ON DEL PEZZO FIBRATIONS IN POSITIVE CHARACTERISTIC J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-03-30 Fabio Bernasconi; Hiromu Tanaka
We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable sections with explicit bounded degree. To prove these results, we study log del Pezzo surfaces defined over imperfect fields.
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RELATIVE UNITARY RZ-SPACES AND THE ARITHMETIC FUNDAMENTAL LEMMA J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-03-24 Andreas Mihatsch
We prove a comparison isomorphism between certain moduli spaces of $p$ -divisible groups and strict ${\mathcal{O}}_{K}$ -modules (RZ-spaces). Both moduli problems are of PEL-type (polarization, endomorphism, level structure) and the difficulty lies in relating polarized $p$ -divisible groups and polarized strict ${\mathcal{O}}_{K}$ -modules. We use the theory of relative displays and frames, as developed
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ISOMORPHISMS UP TO BOUNDED TORSION BETWEEN RELATIVE K0-GROUPS AND CHOW GROUPS WITH MODULUS J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-03-18 RYOMEI IWASA; WATARU KAI
The purpose of this note is to establish isomorphisms up to bounded torsion between relative K0-groups and Chow groups with modulus as defined by Binda and Saito.
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PROPAGATION OF SINGULARITIES ON A S SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION J. Inst. Math. Jussieu (IF 1.254) Pub Date : 2020-03-18 Oran Gannot; Michał Wrochna
We consider the Klein–Gordon equation on asymptotically anti-de-Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularizing terms, of parametrices