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• The asymptotics of ECH capacities AI翻译
  作者：Cristofaro-Gardiner, Daniel; Hutchings, Michael; Ramos, Vinicius Gripp Barros
  作者单位：Institute for Advanced Study - USA; University of California System; University of California Berkeley; Nantes Universite
  摘要：In a previous paper, the second author used embedded contact homology (ECH) of contact three-manifolds to define ECH capacities of four-dimensional symplectic manifolds. In the present paper we prove that for a four-dimensional Liouville domain with all ECH capacities finite, the asymptotics of the ECH capacities recover the symplectic volume. This follows from a more general theorem relating the volume of a contact three-manifold to the asymptotics of the amount of symplectic action needed to...
• On the birational section conjecture with local conditions AI翻译
  作者：Stix, Jakob
  作者单位：Goethe University Frankfurt
  摘要：A birationally liftable Galois section of a hyperbolic curve over a number field yields an adelic point of the smooth completion . We show that is -integral outside a set of places of Dirichlet density , or is cuspidal. The proof relies on -quotients of for some open . If is totally real or imaginary quadratic, we prove that all birationally adelic, non-cuspidal Galois sections come from rational points as predicted by the section conjecture of anabelian geometry. As an aside we also obtain a ...
• Countable abelian group actions and hyperfinite equivalence relations AI翻译
  作者：Gao, Su; Jackson, Steve
  作者单位：University of North Texas System; University of North Texas Denton
  摘要：An equivalence relation E on a standard Borel space is hyperfinite if E is the increasing union of countably many Borel equivalence relations where all -equivalence classs are finite. In this article we establish the following theorem: if a countable abelian group acts on a standard Borel space in a Borel manner then the orbit equivalence relation is hyperfinite. The proof uses constructions and analysis of Borel marker sets and regions in the space This technique is also applied to a problem ...
• Holomorphic arcs on singularities AI翻译
  作者：Kollar, Janos; Nemethi, Andras
  作者单位：Princeton University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
  摘要：The study of formal arcs was initiated by Nash in a 1967 preprint. Arc spaces of smooth varieties have a rather transparent structure but difficult problems arise for arcs passing through singularities. The Nash conjecture on the irreducible components of such arc spaces was proved for surfaces by Fernandez de Bobadilla and Pe Pereira and for toric singularities by Ishii and Kollar, but counter examples were found in higher dimensions by Ishii and Kollar, de Fernex and Johnson and Kollar. Here...
• The topology of rationally and polynomially convex domains AI翻译
  作者：Cieliebak, Kai; Eliashberg, Yakov
  作者单位：University of Augsburg; Stanford University
  摘要：We give in this article necessary and sufficient conditions on the topology of a compact domain with smooth boundary in C-n, n >= 3, to be isotopic to a rationally or polynomially convex domain.
• Heights of Kudla-Rapoport divisors and derivatives of -functions AI翻译
  作者：Bruinier, Jan Hendrik; Howard, Benjamin; Yang, Tonghai
  作者单位：Technical University of Darmstadt; Boston College; University of Wisconsin System; University of Wisconsin Madison
  摘要：We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature . We construct an arithmetic theta lift from harmonic Maass forms of weight to the arithmetic Chow group of the integral model of a unitary Shimura variety, by associating to a harmonic Maass form a linear combination of Kudla-Rapoport divisors, equipped with the Green function given by the regularized theta lift of . Our main result is an equality of two complex numbers: (1) ...
• Hyperbolic groups with planar boundaries AI翻译
  作者：Haissinsky, Peter
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：We prove that the class of convex-cocompact Kleinian groups is quasi-isometrically rigid. We also establish that a word hyperbolic group with a planar boundary different from the sphere is virtually a convex-cocompact Kleinian group provided that its boundary has Ahlfors regular conformal dimension strictly less than 2 or if it acts geometrically on a CAT(0) cube complex.
• A point in a nd-polytope is the barycenter of n points in its d-faces AI翻译
  作者：Dobbins, Michael Gene
  作者单位：Pohang University of Science & Technology (POSTECH)
  摘要：Using equivariant topology, we prove that it is always possible to find points in the -dimensional faces of a -dimensional convex polytope so that their center of mass is a target point in . Equivalently, the -fold Minkowski sum of a -polytope's -skeleton is that polytope scaled by . This verifies a conjecture by Takeshi Tokuyama.
• The Tate conjecture for surfaces over finite fields (vol 194, pg 119, 2013) AI翻译
  作者：Charles, Francois
  作者单位：Universite Paris Saclay
• Equidistribution from fractal measures AI翻译
  作者：Hochman, Michael; Shmerkin, Pablo
  作者单位：University of Surrey
  摘要：We give a fractal-geometric condition for a measure on to be supported on points that are normal in base , i.e. such that equidistributes modulo 1. This condition is robust under coordinate changes, and it applies also when is a Pisot number rather than an integer. As applications we obtain new results (and strengthen old ones) about the prevalence of normal numbers in fractal sets, and new results on measure rigidity, specifically completing Host's theorem to multiplicatively independent inte...