Inventiones mathematicae

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• The logarithmic gauged linear sigma model AI翻译
  作者：Chen, Qile; Janda, Felix; Ruan, Yongbin
  作者单位：Boston College; University of Notre Dame; Zhejiang University
  摘要：We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation of a new technique for computing higher genus Gromov-...
• Supersingular K3 surfaces are unirational (vol 200, pg 979, 2015) AI翻译
  作者：Liedtke, Christian
  作者单位：Technical University of Munich
  摘要：As was pointed out by Bragg and Lieblich
• A Dichotomy for the Weierstrass-type functions AI翻译
  作者：Ren, Haojie; Shen, Weixiao
  作者单位：Fudan University; Fudan University
  摘要：For a real analytic periodic function phi : R -> R, an integer b >= 2 and lambda is an element of (1/b, 1), we prove the following dichotomy for the Weierstrass-type function W(x) = Sigma(n >=)0 lambda(n)phi(b(n)x): Either W(x) is real analytic, or the Hausdorff dimension of its graph is equal to 2 + log(b) lambda. Furthermore, given b and phi, the former alternative only happens for finitely many lambda unless phi is constant.
• A counterexample to vanishing conjectures for negative K-theory AI翻译
  作者：Neeman, Amnon
  作者单位：Australian National University
  摘要：In a 2006 article Schlichting conjectured that the negative K-theory of any abelian category must vanish. This conjecture was generalized in a 2019 article by Antieau, Gepner and Heller, who hypothesized that the negative K-theory of any category with a bounded t-structure must vanish. Both conjectures will be shown to be false.
• Higher order corks AI翻译
  作者：Melvin, Paul; Schwartz, Hannah
  作者单位：Bryn Mawr College; Princeton University
  摘要：It is shown that any finite list of smooth closed simply-connected 4-manifolds homeomorphic to a given oneXcan be obtained by removing a single compact contractible submanifold (orcork) fromX, and then regluing it by powers of a boundary diffeomorphism. We then use this result to 'separate' finite families of corks embedded in a fixed 4-manifold.
• A complexity problem for Borel graphs AI翻译
  作者：Todorcevic, Stevo; Vidnyanszky, Zoltan
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; University of Toronto; California Institute of Technology
  摘要：We show that there is no simple (e.g. finite or countable) basis for Borel graphs with infinite Borel chromatic number. In fact, it is proved that the closed subgraphs of the shift graph on [N](N) with finite (or, equivalently, <= 3) Borel chromatic number form a Sigma(1)(2)-complete set. This answers a question of Kechris and Marks and strengthens several earlier results.
• Correlation energy of a weakly interacting Fermi gas AI翻译
  作者：Benedikter, Niels; Nam, Phan Thanh; Porta, Marcello; Schlein, Benjamin; Seiringer, Robert
  作者单位：University of Milan; University of Munich; International School for Advanced Studies (SISSA); University of Zurich; Institute of Science & Technology - Austria
  摘要：We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a ne...
• Plancherel formula for GLn(F)\GLn(E) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups AI翻译
  作者：Beuzart-Plessis, Raphael
  作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
  摘要：We establish an explicit Plancherel decomposition for GL(n)(F)\GL(n)(E) where E/F is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai gamma-factors. We also give two applications of this Plancherel formula: first to the global Ichino-Ikeda conjecture for unitary groups by completing a comparison between local relative characters that was left open by Zhang (J Am Math Soc 27:541-612, 2014) and secondly to the Hiraga-Ichino-Ikeda ...
• Conjectures and results about parabolic induction of representations of GLn(F) AI翻译
  作者：Lapid, Erez; Minguez, Alberto
  作者单位：Weizmann Institute of Science; University of Vienna
  摘要：In 1980 Zelevinsky introduced certain commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction. The conditions are in the spirit of the Geiss-Leclerc-Schroer condition that occurs in the conjectural...
• Equidistribution of expanding translates of curves and Diophantine approximation on matrices AI翻译
  作者：Yang, Pengyu
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We study the general problem of equidistribution of expanding translates of an analytic curve by an algebraic diagonal flow on the homogeneous space G/Gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G/\Gamma $$\end{document} of a semisimple algebraic group G. We define two families of algebraic subvarieties of...