2013

最新文章

• 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...
• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov) AI翻译
  作者：Vasy, Andras
  作者单位：Stanford University
  摘要：In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable under perturbations. This framework, described in Sect. 2, resides on a compact manifold without boundary, hence in the standard setting of microlocal analysis. Many natural applications arise in the setting of non-Riemannian b-metrics in the context of Melrose's b-structures. These include asymptotically de...
• Spectral shift function of higher order AI翻译
  作者：Potapov, Denis; Skripka, Anna; Sukochev, Fedor
  作者单位：University of New South Wales Sydney; University of New Mexico
  摘要：This paper resolves affirmatively Koplienko's (Sib. Mat. Zh. 25:62-71, 1984) conjecture on existence of higher order spectral shift measures. Moreover, the paper establishes absolute continuity of these measures and, thus, existence of the higher order spectral shift functions. A spectral shift function of order naacenter dot is the function eta (n) =eta (n,H,V) such that for every sufficiently smooth function f, where H is a self-adjoint operator defined in a separable Hilbert space ai and V ...
• The main conjecture of Iwasawa theory for totally real fields AI翻译
  作者：Kakde, Mahesh
  作者单位：University of London; King's College London
  摘要：Let p be an odd prime. Let be a compact p-adic Lie group with a quotient isomorphic to acurrency sign (p) . We give an explicit description of K (1) of the Iwasawa algebra of in terms of Iwasawa algebras of Abelian subquotients of . We also prove a result about K (1) of a certain canonical localisation of the Iwasawa algebra of , which occurs in the formulation of the main conjectures of noncommutative Iwasawa theory. These results predict new congruences between special values of Artin L-func...
• The Hesselink stratification of nullcones and base change AI翻译
  作者：Clarke, Matthew C.; Premet, Alexander
  作者单位：University of Cambridge; University of Manchester
  摘要：Let G be a connected reductive algebraic group over an algebraically closed field of characteristic pa parts per thousand yen0. We give a case-free proof of Lusztig's conjectures (Lusztig in Transform. Groups 10:449-487, 2005) on so-called unipotent pieces. This presents a uniform picture of the unipotent elements of G which can be viewed as an extension of the Dynkin-Kostant theory, but is valid without restriction on p. We also obtain analogous results for the adjoint action of G on its Lie ...