Inventiones mathematicae

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• Rigidity of CR maps between Shilov boundaries of bounded symmetric domains AI翻译
  作者：Kim, Sung-Yeon; Zaitsev, Dmitri
  作者单位：Kangwon National University; Trinity College Dublin
  摘要：Our goal is to establish what seems to be the first rigidity result for CR embeddings between Shilov boundaries of bounded symmetric domains of higher rank. The result states that any such CR embedding is the standard linear embedding up to CR automorphisms. Our basic assumption extends precisely the well-known optimal bound for the rank one case. There are no other restrictions on the ranks, in particular, the difficult case when the target rank is larger than the source rank is also allowed.
• Several consequences of the worths of Arthur for the spectrum and the topology of hyperbolic manifolds AI翻译
  作者：Bergeron, Nicolas; Clozel, Laurent
  作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• Bounds on the density of states for Schrodinger operators AI翻译
  作者：Bourgain, Jean; Klein, Abel
  作者单位：Institute for Advanced Study - USA; University of California System; University of California Irvine
  摘要：We establish bounds on the density of states measure for Schrodinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a density of states outer-measure that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-Holder continuity for this density of states outer-measure in one, two, and three d...
• The Local Langlands Correspondence for GLn over p-adic fields AI翻译
  作者：Scholze, Peter
  作者单位：University of Bonn
  摘要：We extend our methods from Scholze (Invent. Math. 2012, doi:10.1007/s00222-012-0419-y) to reprove the Local Langlands Correspondence for GL (n) over p-adic fields as well as the existence of l-adic Galois representations attached to (most) regular algebraic conjugate self-dual cuspidal automorphic representations, for which we prove a local-global compatibility statement as in the book of Harris-Taylor (The Geometry and Cohomology of Some Simple Shimura Varieties, 2001). In contrast to the pro...
• On arithmetic models and functoriality of Bost-Connes systems. With an appendix by Sergey Neshveyev AI翻译
  作者：Yalkinoglu, Bora
  作者单位：Max Planck Society
  摘要：This paper has two parts. In the first part we construct arithmetic models of Bost-Connes systems for arbitrary number fields, which has been an open problem since the seminal work of Bost and Connes (Sel. Math. 1(3): 411-457, 1995). In particular our construction shows how the class field theory of an arbitrary number field can be realized through the dynamics of a certain operator algebra. This is achieved by working in the framework of Endomotives, introduced by Connes, Consani and Marcolli...
• Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics AI翻译
  作者：Popovici, Dan
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：This paper is intended to start a series of works aimed at proving that if in a (smooth) complex analytic family of compact complex manifolds all the fibres, except one, are supposed to be projective, then the remaining (limit) fibre must be Moishezon. A new method of attack, whose starting point originates in Demailly's work, is introduced. While we hope to be able to address the general case in the near future, two important special cases are established here: the one where the Hodge numbers...
• Lattices, graphs, and Conway mutation AI翻译
  作者：Greene, Joshua Evan
  作者单位：Boston College
  摘要：The d-invariant of an integral, positive definite lattice I > records the minimal norm of a characteristic covector in each equivalence class . We prove that the 2-isomorphism type of a connected graph is determined by the d-invariant of its lattice of integral flows (or cuts). As an application, we prove that a reduced, alternating link diagram is determined up to mutation by the Heegaard Floer homology of the link's branched double-cover. Thus, alternating links with homeomorphic branched do...
• Dirichlet fundamental domains and topology of projective varieties AI翻译
  作者：Kapovich, Michael
  作者单位：University of California System; University of California Davis
  摘要：We prove that for every finitely-presented group G there exists a 2-dimensional irreducible complex-projective variety W with the fundamental group G, so that all singularities of W are normal crossings and Whitney umbrellas.
• Rotational symmetry of self-similar solutions to the Ricci flow AI翻译
  作者：Brendle, Simon
  作者单位：Stanford University
  摘要：Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.
• Dedekind zeta motives for totally real number fields AI翻译
  作者：Brown, Francis C. S.
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
  摘要：Let k be a totally real number field. For every odd na parts per thousand yen3, we construct an element in the category MT(k) of mixed Tate motives over k out of the quotient of a product of hyperbolic spaces by an arithmetic group. By a volume calculation, we prove that its period is a rational multiple of , where denotes the special value of the Dedekind zeta function of k. We deduce that the group is generated by the cohomology of a quadric relative to hyperplanes, and that is a determinant...