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• Unique ergodicity for foliations in P2 with an invariant curve AI翻译
  作者：Dinh, Tien-Cuong; Sibony, Nessim
  作者单位：National University of Singapore; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
  摘要：Consider a foliation in the projective plane admitting a projective line as the unique invariant algebraic curve. Assume that the foliation is generic in the sense that its singular points are hyperbolic. We show that there is a unique positive dd(c)-closed (1, 1)-current of mass 1 which is directed by the foliation and this is the current of integration on the invariant line. A unique ergodicity theorem for the distribution of leaves follows: for any leaf L, appropriate averages of L converge...
• Global rigid inner forms and multiplicities of discrete automorphic representations AI翻译
  作者：Kaletha, Tasho
  摘要：We study the cohomology of certain Galois gerbes over number fields. This cohomology provides a bridge between refined local endoscopy, as introduced in Kaletha (Ann Math (2) 184(2):559-632, 2016), and classical global endoscopy. As particular applications, we express the canonical adelic transfer factor that governs the stabilization of the Arthur-Selberg trace formula as a product of normalized local transfer factors, we give an explicit constriction of the pairing between an adelic L-packet...
• On the nature of the generating series of walks in the quarter plane AI翻译
  作者：Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F.
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); North Carolina State University
  摘要：In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many of the recent results about these series, but also to go beyond them. For instance, we give for the first time hypertranscendency results, i.e., we prove that certain of these generating series do not satisfy any nontrivial nonlinear algebraic differential eq...
• Kirwan surjectivity for quiver varieties AI翻译
  作者：McGerty, Kevin; Nevins, Thomas
  作者单位：University of Oxford; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：For algebraic varieties defined by hyperkahler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the hyperkahler Kirwan map on cohomology is surjective. We resolve this question in the affirmative for Nakajima quiver varieties. We also establish similar results for other cohomology theories and for the derived category. Our proofs use only classical topological and geometric arguments.
• Reductive groups, the loop Grassmannian, and the Springer resolution AI翻译
  作者：Achar, Pramod N.; Riche, Simon
  作者单位：Louisiana State University System; Louisiana State University; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper we prove equivalences of categories relating the derived category of a block of the category of representations of a connected reductive algebraic group over an algebraically closed field of characteristic p bigger than the Coxeter number and a derived category of equivariant coherent sheaves on the Springer resolution (or a parabolic counterpart). In the case of the principal block, combined with previous results, this provides a modular version of celebrated constructions due t...
• Modularity lifting beyond the Taylor-Wiles method AI翻译
  作者：Calegari, Frank; Geraghty, David
  作者单位：University of Chicago; Boston College
  摘要：We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor-Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology. In practice, this imposes several restrictions-one must be in a Shimura variety setting and the automorphic forms must be of regular weight at infinity. In this paper, we essentially show h...
• Attracting currents and equilibrium measures for quasi-attractors of AI翻译
  作者：Taflin, Johan
  作者单位：Universite Bourgogne Europe
  摘要：Let f be a holomorphic endomorphism of of degree d. For each quasi-attractor of f we construct a finite set of currents with attractive behaviors. To every such attracting current is associated an equilibrium measure which allows for a systematic ergodic theoretical approach in the study of quasi-attractors of . As a consequence, we deduce that there exist at most countably many quasi-attractors, each one with topological entropy equal to a multiple of . We also show that the study of these an...
• Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid AI翻译
  作者：Glass, Olivier; Munnier, Alexandre; Sueur, Franck
  作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Inria; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
  摘要：The point vortex system is usually considered as an idealized model where the vorticity of an ideal incompressible two-dimensional fluid is concentrated in a finite number of moving points. In the case of a single vortex in an otherwise irrotational ideal fluid occupying a bounded and simply-connected two-dimensional domain the motion is given by the so-called Kirchhoff-Routh velocity which depends only on the domain. The main result of this paper establishes that this dynamics can also be obt...
• Corrigendum to Neron models, Lie algebras, and reduction of curves of genus one and The Brauer group of a surface AI翻译
  作者：Liu, Qing; Lorenzini, Dino; Raynaud, Michel
  作者单位：Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; CNRS - National Institute for Mathematical Sciences (INSMI); University System of Georgia; University of Georgia; Universite Paris Saclay
• Quadratic forms and systems of forms in many variables AI翻译
  作者：Myerson, Simon L. Rydin
  作者单位：University of London; University College London
  摘要：Let be quadratic forms with integer coefficients in n variables. When and the variety is a smooth complete intersection, we prove an asymptotic formula for the number of integer points in an expanding box at which these forms simultaneously vanish, which in particular implies the Hasse principle for . Previous work in this direction required n to grow at least quadratically with R. We give a similar result for R forms of degree d, conditional on an upper bound for the number of solutions to an...