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Which magnetic fields support a zero mode? J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-28 Rupert L. Frank,Michael Loss
Abstract This paper presents some results concerning the size of magnetic fields that support zero modes for the three-dimensional Dirac equation and related problems for spinor equations. It is a well-known fact that for the Schrödinger equation in three dimensions to have a negative energy bound state, the 3 / 2 {3/2} norm of the potential has to be greater than the Sobolev constant. We prove an
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Skein lasagna modules for 2-handlebodies J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-28 Ciprian Manolescu,Ikshu Neithalath
Abstract Morrison, Walker, and Wedrich used the blob complex to construct a generalization of Khovanov–Rozansky homology to links in the boundary of a 4-manifold. The degree zero part of their theory, called the skein lasagna module, admits an elementary definition in terms of certain diagrams in the 4-manifold. We give a description of the skein lasagna module for 4-manifolds without 1- and 3-handles
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Kazhdan–Lusztig conjecture via zastava spaces J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-20 Alexander Braverman,Michael Finkelberg,Hiraku Nakajima
Abstract We deduce the Kazhdan–Lusztig conjecture on the multiplicities of simple modules over asimple complex Lie algebra in Verma modules in category 𝒪 {\mathcal{O}} from the equivariantgeometric Satake correspondence and the analysis of torus fixed points in zastava spaces.We make similar speculations for the affine Lie algebras and 𝒲 {\mathscr{W}} -algebras.
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Hyperbolic secant varieties of M-curves J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-20 Mario Kummer,Rainer Sinn
Abstract We relate the geometry of curves to the notion of hyperbolicity in real algebraic geometry. A hyperbolic variety is a real algebraic variety that (in particular) admits a real fibered morphism to a projective space whose dimension is equal to the dimension of the variety. We study hyperbolic varieties with a special interest in the case of hypersurfaces that admit a real algebraic ruling.
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On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-20 Xiao-Lei Liu,Sheng-Li Tan
Abstract Modular invariantsof families of curves are Arakelov invariants in arithmetic algebraic geometry. All the known uniform lower bounds of these invariants are not sharp. In this paper, we aim to give explicit lower bounds of modular invariants of families of curves, which is sharp for genus 2. According to the relation between fractional Dehn twists and modular invariants, we give the sharp
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Noether–Severi inequality and equality for irregular threefolds of general type J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-20 Yong Hu,Tong Zhang
Abstract We prove the optimal Noether–Severi inequality that vol ( X ) ≥ 4 3 χ ( ω X ) {\operatorname{vol}(X)\geq\frac{4}{3}\chi(\omega_{X})} for all smooth and irregular 3-folds X of general type over ℂ {\mathbb{C}} .For those 3-folds X attaining the equality, we completely describe their canonical models and show that the topological fundamental group π 1 ( X ) ≃ ℤ 2 {\pi_{1}(X)\simeq\mathbb{Z}^{2}}
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Artin–Mazur heights and Yobuko heights of proper log smooth schemes of Cartier type, and Hodge–Witt decompositions and Chow groups of quasi-F-split threefolds J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-20 Yukiyoshi Nakkajima
Abstract Let X / s {X/s} be a proper log smooth scheme of Cartier type overa fine log scheme whose underlying scheme isthe spectrum of a perfect field κ of characteristic p > 0 {p>0} .In this article we prove that the cohomology of 𝒲 ( 𝒪 X ) {{\mathcal{W}}({\mathcal{O}}_{X})} is a finitely generated 𝒲 ( κ ) {{\mathcal{W}}(\kappa)} -moduleif the Yobuko height of X is finite.As an application
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Degeneration of curves on some polarized toric surfaces J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-01 Karl Christ,Xiang He,Ilya Tyomkin
Abstract We address the following question:Given a polarized toric surface ( S , L ) {(S,{\mathcal{L}})} , and a general integral curve C of geometric genus g in the linear system | L | {|{\mathcal{L}}|} , do there exist degenerations of C in | L | {|{\mathcal{L}}|} to general integral curves of smaller geometric genera? We give an affirmative answer to this question for surfaces associated to h-transverse
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Monodromic model for Khovanov–Rozansky homology J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-01 Roman Bezrukavnikov,Kostiantyn Tolmachov
Abstract We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild cohomology groups (for the zero and the top degree cohomology this reduces to an earlier result of Gorsky, Hogancamp, Mellit and Nakagane). These objects
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CMC hypersurfaces with bounded Morse index J. reine angew. Math. (IF 1.5) Pub Date : 2022-04-01 Theodora Bourni,Ben Sharp,Giuseppe Tinaglia
Abstract We provide qualitative bounds on the area and topology of separating constant mean curvature (CMC) surfaces of bounded (Morse) index. We also develop a suitable bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular, we show that convergence always occurs with multiplicity one, which implies that
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Nguyen’s tridents and the classification of semigraphical translators for mean curvature flow J. reine angew. Math. (IF 1.5) Pub Date : 2022-03-01 David Hoffman,Francisco Martín,Brian White
Abstract We construct a one-parameter family of singly periodic translating solutions to meancurvature flow that converge as the period tends to 0 to the union of a grim reaper surfaceand a plane that bisects it lengthwise. The surfaces are semigraphical: they are properly embedded,and, after removing a discretecollection of vertical lines, they are graphs.We also provide a nearly complete classification
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Corrigendum to Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space (J. reine angew. Math. 727 (2017), 269–299) J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-25 Lan-Hsuan Huang,Dan A. Lee,Christina Sormani
Abstract There is an error in the proof of Theorem 1.3 of the original article.Despite the problem, it is rigorously proved in joint work of the first two authors and Perales that Theorem 1.3 is true, using recent results of Allen and Perales that extend the work of Allen, Perales, and Sormani.
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Connectedness of Kisin varieties associated to absolutely irreducible Galois representations J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-25 Miaofen Chen,Sian Nie
Abstract We consider the Kisin variety associated to an n-dimensional absolutely irreducible mod p Galois representation ρ ¯ {\bar{\rho}} of a p-adic field K together with a cocharacter μ. Kisin conjectured that the Kisin variety is connected in this case. We show that Kisin’s conjecture holds if K is totally ramified with n = 3 {n=3} or μ is of a very particular form. As an application, we get a connectedness
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The Lawson surfaces are determined by their symmetries and topology J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-25 Nikolaos Kapouleas,David Wiygul
Abstract We prove that a closed embedded minimal surface in the round three-sphere which satisfies the symmetries of a Lawson surface and has the same genus is congruent to the Lawson surface.
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Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-25 Benoît Claudon,Patrick Graf,Henri Guenancia,Philipp Naumann
Abstract Let X be a compact Kähler space with klt singularities and vanishing first Chern class.We prove the Bochner principle for holomorphic tensors on the smooth locus of X: any such tensor is parallel with respect to the singular Ricci-flat metrics.As a consequence, after a finite quasi-étale cover X splits off a complex torus of the maximum possible dimension.We then proceed to decompose the tangent
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K-stability of cubic fourfolds J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-25 Yuchen Liu
Abstract We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space.More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the corresponding GIT stabilities, which was studied in detail by Laza. In particular, this implies that all smooth cubic fourfolds admit Kähler–Einstein metrics. Key ingredients are local volume estimates in dimension three due
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A description of monodromic mixed Hodge modules J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-25 Takahiro Saito
Abstract For a smooth algebraic variety X, a monodromic D-module on X × ℂ {X\times\mathbb{C}} is decomposed into a direct sum of some D-modules on X.We show that the Hodge filtration of a mixed Hodge module on X × ℂ {X\times\mathbb{C}} whose underlying D-module is monodromic is also decomposed.Moreover, we show that there is an equivalence of categories between the category of monodromic mixed Hodge
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Simultaneous supersingular reductions of CM elliptic curves J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-25 Menny Aka,Manuel Luethi,Philippe Michel,Andreas Wieser
Abstract We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication.We show – under additional congruence assumptions on the CM order – that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order becomes large.This variant of the equidistribution theorems of Duke
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The Neukirch–Uchida theorem with restricted ramification J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-15 Ryoji Shimizu
Abstract Let K be a number field and S a set of primes of K.We write K S / K {K_{S}/K} for the maximal extension of Kunramified outside S and G K , S {G_{K,S}} for its Galois group.In this paper, we prove the following generalization of the Neukirch–Uchida theorem under some assumptions:“For i = 1 , 2 {i=1,2} , let K i {K_{i}} be a number field and S i {S_{i}} a set of primes of K i {K_{i}} . If G
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Perverse 𝔽 p -sheaves on the affine Grassmannian J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-15 Robert Cass
Abstract For a reductive group over an algebraically closed field of characteristic p > 0 {p>0} we construct the abelian category of perverse 𝔽 p {\mathbb{F}_{p}} -sheaves on the affine Grassmannian that are equivariant with respect to the action of the positive loop group. We show this is a symmetric monoidal category, and then we apply a Tannakian formalism to show this category is equivalent to
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The Hilbert–Schinzel specialization property J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-15 Arnaud Bodin,Pierre Dèbes,Joachim König,Salah Najib
Abstract We establish a version “over the ring” ofthe celebrated Hilbert Irreducibility Theorem. Given finitely many polynomials in k + n {k+n} variables,with coefficients in ℤ {\mathbb{Z}} , of positive degree in the last n variables, we show that if they are irreducible over ℤ {\mathbb{Z}} and satisfy a necessary “Schinzel condition”, then the first k variables can be specialized in a Zariski-dense
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Isomorphisms among quantum Grothendieck rings and propagation of positivity J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-15 Ryo Fujita,David Hernandez,Se-jin Oh,Hironori Oya
Abstract Let ( 𝔤 , 𝗀 ) {\mathfrak{g},\mathsf{g})} be a pair of complex finite-dimensional simple Lie algebras whoseDynkin diagrams are related by (un)folding, with 𝗀 {\mathsf{g}} being of simply-laced type.We construct a collection of ring isomorphismsbetween the quantum Grothendieck ringsof monoidal categories 𝒞 𝔤 {\mathscr{C}_{\mathfrak{g}}} and 𝒞 𝗀 {\mathscr{C}_{\mathsf{g}}} offinite-dimensional
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A central limit theorem for integrals of random waves J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-15 Matthew de Courcy-Ireland,Marius Lemm
Abstract We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of dimension 3 or higher, thanks to the universality of the local Weyl law. The key technical step is an estimate capturing some cancellation in a triple integral of Bessel functions, which we achieve using Gegenbauer’s
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A mixed elliptic-parabolic boundary value problem coupling a harmonic-like map with a nonlinear spinor J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-15 Jürgen Jost,Lei Liu,Miaomiao Zhu
Abstract In this paper, we solve a new elliptic-parabolic system arising in geometric analysis that is motivated by the nonlinear supersymmetric sigma model of quantum field theory. The corresponding action functional involves two fields, a map from a Riemann surface into a Riemannian manifold and a spinor coupled to the map. The first field has to satisfy a second-order elliptic system, which we turn
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Frontmatter J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01
Article Frontmatter was published on February 1, 2022 in the journal Journal für die reine und angewandte Mathematik (volume 2022, issue 783).
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An explicit formula for the Siegel series of a quadratic form over a non-archimedean local field J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Tamotsu Ikeda, Hidenori Katsurada
Let F be a non-archimedean local field of characteristic 0, and 𝔬{{\mathfrak{o}}} the ring of integers in F . We give an explicit formula for the Siegel series of a half-integral matrix over 𝔬{{\mathfrak{o}}}. This formula expresses the Siegel series of a half-integral matrix B explicitly in terms of the Gross–Keating invariant of B and its related invariants.
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Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case) J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Kei Yuen Chan
We prove a local Gan–Gross–Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean fields. We also generalize to Bessel and Fourier–Jacobi models and study a possible generalization to Ext-branching laws.
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Prescribing Ricci curvature on homogeneous spaces J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Jorge Lauret, Cynthia E. Will
The prescribed Ricci curvature problem in the context of G -invariant metrics on a homogeneous space M=G/K{M=G/K} is studied. We focus on the metrics at which the map g↦Rc(g){g\mapsto\operatorname{Rc}(g)} is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in
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Self-similar solutions to fully nonlinear curvature flows by high powers of curvature J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Shanze Gao, Haizhong Li, Xianfeng Wang
In this paper, we investigate closed strictly convex hypersurfaces in ℝn+1{\mathbb{R}^{n+1}} which shrink self-similarly under a large family of fully nonlinear curvature flows by high powers of curvature. When the speed function is given by powers of a homogeneous of degree 1 and inverse concave function of the principal curvatures with power greater than 1, we prove that the only such hypersurfaces
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Ricci flow on manifolds with boundary with arbitrary initial metric J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Tsz-Kiu Aaron Chow
In this paper, we study the Ricci flow on manifolds with boundary. In the paper, we substantially improve Shen’s result [Y. Shen, On Ricci deformation of a Riemannian metric on manifold with boundary, Pacific J. Math. 173 1996, 1, 203–221] to manifolds with arbitrary initial metric. We prove short-time existence and uniqueness of the solution, in which the boundary becomes instantaneously totally geodesic
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Unbounded negativity on rational surfaces in positive characteristic J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Raymond Cheng, Remy van Dobben de Bruyn
We give explicit blowups of the projective plane in positive characteristic that contain smooth rational curves of arbitrarily negative self-intersection, showing that the Bounded Negativity Conjecture fails even for rational surfaces in positive characteristic. As a consequence, we show that any surface in positive characteristic admits a birational model failing the Bounded Negativity Conjecture
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Extending torsors on the punctured Spec(Ainf) J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Johannes Anschütz
We prove that torsors under parahoric group schemes on the punctured spectrum of Fontaine’s ring Ainf{A_{\mathrm{inf}}}, extend to the whole spectrum. Using descent we can extend a similar result for the ring 𝔖{\mathfrak{S}} of Kisin and Pappas to full generality. Moreover, we treat similarly the case of equal characteristic. As applications we extend results of Ivanov on exactness of the loop functor
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Non-isomorphic 2-groups with isomorphic modular group algebras J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Diego García-Lucas, Leo Margolis, Ángel del Río
We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.
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Erratum to Profinite rigidity for twisted Alexander polynomials (J. reine angew. Math. 771 (2021), 171–192) J. reine angew. Math. (IF 1.5) Pub Date : 2022-02-01 Jun Ueki
We clarify the definition of the divisorial hull and recollect some basic facts. Then we correct Lemma 4.2 and Theorem 11.2 (1)–(2) in the original article.
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The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups J. reine angew. Math. (IF 1.5) Pub Date : 2022-01-27 Vasileios Chousionis,Sean Li,Robert Young
Abstract We show that the β-numbers of intrinsic Lipschitz graphs of Heisenberg groups ℍ n {\mathbb{H}_{n}} are locally Carleson integrable when n ≥ 2 {n\geq 2} . Our main bound uses a novel slicing argument to decompose intrinsic Lipschitz graphs into graphs of Lipschitz functions. A key ingredient in our proof is a Euclidean inequality that bounds the β-numbers of the original graph in terms of the
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Numerical equivalence of ℝ-divisors and Shioda–Tate formula for arithmetic varieties J. reine angew. Math. (IF 1.5) Pub Date : 2022-01-27 Paolo Dolce,Roberto Gualdi
Abstract Let X be an arithmetic variety over the ring of integers of a number field K, with smooth generic fiber X K {X_{K}} .We give a formula that relates the dimension of the first Arakelov–Chow vector space of X with the Mordell–Weil rank of the Albanese variety of X K {X_{K}} and the rank of the Néron–Severi group of X K {X_{K}} .This is a higher-dimensional and arithmetic version of the classical
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Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups J. reine angew. Math. (IF 1.5) Pub Date : 2022-01-23 Yoshikazu Yamaguchi
Abstract We show that the absolute value at zero ofthe Ruelle zeta function defined by the geodesic flowcoincides with the higher-dimensional Reidemeister torsionfor the unit tangent bundle over a 2-dimensional hyperbolic orbifoldand a non-unitary representation of the fundamental group.Our proof is based on the integral expression of the Ruelle zeta function.This integral expression is derived from
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The inertial Jacquet–Langlands correspondence J. reine angew. Math. (IF 1.5) Pub Date : 2022-01-23 Andrea Dotto
Abstract We give a parametrization of the simple Bernstein components of inner forms of a general linear group over a local field by two invariants constructed from type theory, and explicitly describe its behaviour under the Jacquet–Langlands correspondence. Along the way, we prove a conjecture of Broussous, Sécherre and Stevens on preservation of endo-classes.
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Total mean curvature of the boundary and nonnegative scalar curvature fill-ins J. reine angew. Math. (IF 1.5) Pub Date : 2022-01-23 Yuguang Shi,Wenlong Wang,Guodong Wei
Abstract In the first part of this paper, we prove the extensibility of an arbitrary boundary metric to a positive scalar curvature (PSC) metric inside for a compact manifold with boundary, completely solving an open problem due to Gromov (see Question 1.1). Then we introduce a fill-in invariant (see Definition 1.2) and discuss its relationship with the positive mass theorems for asymptotically flat
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Long time behavior of discrete volume preserving mean curvature flows J. reine angew. Math. (IF 1.5) Pub Date : 2022-01-23 Massimiliano Morini,Marcello Ponsiglione,Emanuele Spadaro
Abstract In this paper we analyze the Euler implicit scheme for the volume preserving mean curvature flow.We prove the exponential convergence of the scheme to a finite union of disjoint balls with equal volume for any bounded initial set with finite perimeter.
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Monodromy of elliptic curve convolution, seven-point sheaves of G 2 type, and motives of Beauville type J. reine angew. Math. (IF 1.5) Pub Date : 2022-01-23 Benjamin Collas,Michael Dettweiler,Stefan Reiter,Will Sawin
Abstract We study Tannakian properties of the convolution product of perverse sheaves on elliptic curves. We establish that for certain sheaves with unipotent local monodromy over seven points the corresponding Tannaka group is isomorphic to G 2 {G_{2}} . This monodromy approach generalizes a result of Katz on the existence of G 2 {G_{2}} -motives in the middle cohomology of deformations of Beauville
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Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups J. reine angew. Math. (IF 1.5) Pub Date : 2021-12-02 Sam Shepherd,Daniel J. Woodhouse
Abstract We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups.Let G be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that are not quadratically hanging
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Nonnegative Ricci curvature and escape rate gap J. reine angew. Math. (IF 1.5) Pub Date : 2021-11-12 Jiayin Pan
Abstract Let M be an open n-manifold of nonnegative Ricci curvature and let p ∈ M {p\in M} . We show that if ( M , p ) {(M,p)} has escape rate less than some positive constant ϵ ( n ) {\epsilon(n)} , that is, minimal representing geodesic loops of π 1 ( M , p ) {\pi_{1}(M,p)} escape from any bounded balls at a small linear rate with respect to their lengths, then π 1 ( M , p ) {\pi_{1}(M,p)}
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On the geometry of lattices and finiteness of Picard groups J. reine angew. Math. (IF 1.5) Pub Date : 2021-11-12 Florian Eisele
Abstract Let ( K , 𝒪 , k ) {(K,\mathcal{O},k)} be a p-modular system with k algebraically closed and 𝒪 {\mathcal{O}} unramified, and let Λ be an 𝒪 {\mathcal{O}} -order in a separable K-algebra. We call a Λ-lattice L rigid if Ext Λ 1 ( L , L ) = 0 {{\operatorname{Ext}}^{1}_{\Lambda}(L,L)=0} , in analogy with the definition of rigid modules over a finite-dimensional algebra.By partitioning the Λ-lattices
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Hopf-type theorem for self-shrinkers J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-28 Hilário Alencar,Gregório Silva Neto,Detang Zhou
Abstract In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three-dimensional Euclidean space ℝ 3 {{\mathbb{R}}^{3}} is a round sphere, provided its mean curvature and the norm of the its position vector have an upper bound in terms of the norm of its traceless second fundamental form. The example constructed by Drugan justifies that the hypothesis
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On the torsion values for sections of an elliptic scheme J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-28 Pietro Corvaja,Julian Demeio,David Masser,Umberto Zannier
Abstract We shall consider sections of a complex elliptic scheme ℰ {{{\mathcal{E}}}} over an affine base curve B, and study the points of B where the section takes a torsion value. In particular, we shall relate the distribution in B of these points with the canonical height of the section, proving an integral formula involving a measure on B coming from the so-called Betti map of the section. We shall
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Hyperkähler metrics near Lagrangian submanifolds and symplectic groupoids J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-26 Maxence Mayrand
Abstract The first part of this paper is a generalization of the Feix–Kaledin theorem on the existence of a hyperkähler metric on a neighborhood of the zero section of the cotangent bundle of a Kähler manifold.We show that the problem of constructing a hyperkähler structure on a neighborhood of a complex Lagrangian submanifold in a holomorphic symplectic manifold reduces to the existence of certain
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About every convex set in any generic Riemannian manifold J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-26 Alexander Lytchak,Anton Petrunin
Abstract We give a necessary condition on a geodesic in a Riemannian manifold that can run in some convex hypersurface.As a corollary, we obtain peculiar properties that hold true for every convex set in any generic Riemannian manifold ( M , g ) {(M,g)} .For example, if a convex set in ( M , g ) {(M,g)} is bounded by a smooth hypersurface, then it is strictly convex.
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Locally pro-p contraction groups are nilpotent J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-16 Helge Glöckner,George A. Willis
Abstract The authors have shown previously that every locally pro-pcontraction group decomposes into the direct product of a p-adicanalytic factor and a torsion factor. It has long been known thatp-adic analytic contraction groups are nilpotent. We show herethat the torsion factor is nilpotent too, and hence that everylocally pro-p contraction group is nilpotent.
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VI-modules in non-describing characteristic, part II J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-16 Rohit Nagpal
Abstract We classify all irreducible generic VI {\mathrm{VI}} -modules in non-describing characteristic.Our result degenerates to yield a classification of irreducible generic FI {\mathrm{FI}} -modules in arbitrary characteristic. Equivalently, we provide a complete classification of irreducibles of admissible 𝐆𝐋 ∞ ( 𝔽 q ) {\mathbf{GL}_{\infty}(\mathbb{F}_{q})} -representations in non-describing
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Local-global principles for homogeneous spaces over some two-dimensional geometric global fields J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-16 Diego Izquierdo,Giancarlo Lucchini Arteche
Abstract In this article, we study the obstructions to the local-global principle for homogeneous spaces with connected or abelian stabilizers over finite extensions of the field ℂ ( ( x , y ) ) {\mathbb{C}((x,y))} of Laurent series in two variables over the complex numbers and over function fields of curves over ℂ ( ( t ) ) {\mathbb{C}((t))} . We give examples that prove that the Brauer–Manin
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Obstruction flat rigidity of the CR 3-sphere J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-16 Sean N. Curry,Peter Ebenfelt
Abstract We consider the obstruction flatness problem for small deformations of the standard CR 3-sphere. That rigidity holds for the CR sphere was previously known (in all dimensions) for the case of embeddable CR structures, where it also holds at the infinitesimal level. In the 3-dimensional case, however, a CR structure need not be embeddable.Unlike in the embeddable case, it turns out that in
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Rank functions on triangulated categories J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-16 Joseph Chuang,Andrey Lazarev
Abstract We introduce the notion of a rank function on a triangulated category 𝒞 {\mathcal{C}} which generalizes the Sylvesterrank function in the case when 𝒞 = 𝖯𝖾𝗋𝖿 ( A ) {\mathcal{C}=\mathsf{Perf}(A)} is the perfect derived category of a ring A. We show that rank functions are closely relatedto functors into simple triangulated categories and classifyVerdier quotients into simple triangulated
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Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár J. reine angew. Math. (IF 1.5) Pub Date : 2021-10-16 Yongqiang Liu,Laurenţiu Maxim,Botong Wang
Abstract In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their
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Shortest closed curve to inspect a sphere J. reine angew. Math. (IF 1.5) Pub Date : 2021-09-03 Mohammad Ghomi,James Wenk
Abstract We show that in Euclidean 3-space any closed curve γ which lies outside the unit sphere and contains the sphere within its convex hull has length ≥ 4 π {\geq 4\pi} . Equality holds only when γ is composed of four semicircles of length π, arranged in the shape of a baseball seam, as conjectured byV. A. Zalgaller in 1996.
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Serre–Tate theory for Calabi–Yau varieties J. reine angew. Math. (IF 1.5) Pub Date : 2021-09-03 Piotr Achinger,Maciej Zdanowicz
Abstract Classical Serre–Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multiplicative coordinates. A variant of this theory has been obtained for ordinary K3 surfaces by Nygaard and Ogus. In this paper, we construct
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Representation by sums of unlike powers J. reine angew. Math. (IF 1.5) Pub Date : 2021-09-03 Jianya Liu,Lilu Zhao
Abstract It is proved that all sufficiently large integers n can be represented as n = x 1 2 + x 2 3 + ⋯ + x 13 14 , n=x_{1}^{2}+x_{2}^{3}+\cdots+x_{13}^{14}, where x 1 , … , x 13 {x_{1},\ldots,x_{13}} are positive integers. This improves upon the current recordwith fourteen variables in place of thirteen.
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A support theorem for\break the Hitchin fibration: The case of GL n and K C J. reine angew. Math. (IF 1.5) Pub Date : 2021-09-03 Mark Andrea A. de Cataldo,Jochen Heinloth,Luca Migliorini
Abstract We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GL n {\mathrm{GL}_{n}} over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups.
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Torus actions, maximality, and non-negative curvature J. reine angew. Math. (IF 1.5) Pub Date : 2021-09-03 Christine Escher,Catherine Searle
Abstract Let ℳ 0 n {\mathcal{M}_{0}^{n}} be the class of closed, simply connected, non-negatively curved Riemannian n-manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} , then M is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to 3. As a special