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作者：Rudenko, Daniil
作者单位：University of Chicago
摘要：We study the trigonometry of non-Euclidean tetrahedra using tools from algebraic geometry. We establish a bijection between non-Euclidean tetrahedra and certain rational elliptic surfaces. We interpret the edge lengths and the dihedral angles of a tetrahedron as values of period maps for the corresponding surface. As a corollary we show that the cross-ratio of the exponents of the solid angles of a tetrahedron is equal to the cross-ratio of the exponents of the perimeters of its faces. The Reg...
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作者：Liu, Ruochuan; Wang, Guozhen
作者单位：Peking University; Fudan University
摘要：A Correction to this paper has been published: 10.1007/s00222-022-01134-9
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作者：Delecroix, Vincent; Goujard, Elise; Zograf, Peter; Zorich, Anton
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); Inria; Universite Paris Cite
摘要：We study the combinatorial geometry of a random closed multi-curve on a surface of large genus g and of a random square-tiled surface of large genus g. We prove that primitive components , gamma(1), ...,gamma(k) of a random multicurve m(1)gamma(1) + ... + m(k)gamma(k) represent linearly independent homology cycles with asymptotic probability 1 and that all its weights m(i); are equal to 1 with asymptotic probability root 2/2. We prove analogous properties for random square-tiled surfaces. In p...
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作者：Li, Chao; Zhang, Wei
作者单位：Columbia University; Massachusetts Institute of Technology (MIT)
摘要：We formulate and prove a local arithmetic Siegel-Weil formula for GSpin Rapoport-Zink spaces, which is a precise identity between the arithmetic intersection numbers of special cycles on GSpin Rapoport-Zink spaces and the derivatives of local representation densities of quadratic forms. As a first application, we prove a semi-global arithmetic Siegel-Weil formula as conjectured by Kudla, which relates the arithmetic intersection numbers of special cycles on GSpin Shimura varieties at a place o...
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作者：Choi, Kyeongsu; Haslhofer, Robert; Hershkovits, Or; White, Brian
作者单位：Korea Institute for Advanced Study (KIAS); University of Toronto; Hebrew University of Jerusalem; Stanford University
摘要：In this paper, we prove the mean-convex neighborhood conjecture for neck singularities of the mean curvature flow in R-n(+1) for all n >= 3: we show that if a mean curvature flow {M-t} in Rn+1 has an Sn-1 x R singularity at (x(0), t(0)), then there exists an epsilon = epsilon(x(0), t(0)) > 0 such that M-t boolean AND B(x(0), epsilon) is mean-convex for all t is an element of (t(0)-epsilon(2), t(0)+epsilon(2)). As in the case n = 2, which was resolved by the first three authors in Choi et al. (...
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作者：Liu, Yifeng; Tian, Yichao; Xiao, Liang; Zhang, Wei; Zhu, Xinwen
作者单位：Zhejiang University; Chinese Academy of Sciences; Peking University; Massachusetts Institute of Technology (MIT); California Institute of Technology
摘要：In this article, we study the Beilinson-Bloch-Kato conjecture for motives associated to Rankin-Selberg products of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value of the Rankin-Selberg L-function does not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch-Kato Selmer group constructed ...
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作者：Calegari, Frank; Geraghty, David
作者单位：University of Chicago; Boston College
摘要：A Correction to this paper has been published: 10.1007/s00222-017-0749-x
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作者：Fakhruddin, Najmuddin; Khare, Chandrashekhar; Patrikis, Stefan
作者单位：Tata Institute of Fundamental Research (TIFR); University of California System; University of California Los Angeles; University System of Ohio; Ohio State University
摘要：We prove the modularity of most reducible, odd representations (rho) over bar : Gamma(Q) -> GL(2)(k) with k a finite field of characteristic an odd prime p. This is an analogue of Serre's celebrated modularity conjecture (which con- cerned irreducible, odd representations (rho) over bar : Gamma(Q) -> GL(2)(k)) for reducible, odd representations. Our proof lifts (rho) over bar to an irreducible geometric p-adic representation rho which is known to arise from a newform by results of Skinner-Wile...
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作者：Baudier, Florent P.; Braga, Bruno M.; Farah, Ilijas; Khukhro, Ana; Vignati, Alessandro; Willett, Rufus
作者单位：Texas A&M University System; Texas A&M University College Station; York University - Canada; University of Cambridge; Universite Paris Cite; Sorbonne Universite; University of Hawaii System; University of Hawaii Manoa
摘要：We show that if X and Y are uniformly locally finite metric spaces whose uniform Roe algebras, C-u* (X) and C-u* (Y), are isomorphic as C*-algebras, then X and Y are coarsely equivalent metric spaces. Moreover, we show that coarse equivalence between X and Y is equivalent to Morita equivalence between C-u* (X) and C-u* (Y). As an application, we obtain that if Gamma and Lambda are finitely generated groups, then the crossed products l(infinity)(Gamma) (sic)(r) Gamma and l(infinity)(Lambda) (si...
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作者：Beaudry, Agnes; Goerss, Paul G.; Hopkins, Michael J.; Stojanoska, Vesna
作者单位：University of Colorado System; University of Colorado Boulder; Northwestern University; Harvard University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：The primary goal of this paper is to study Spanier-Whitehead duality in the K (n)-local category. One of the key players in the K (n)-local category is the Lubin-Tate spectrum E-n, whose homotopy groups classify deformations of a formal group law of height n, in the implicit characteristic p. It is known that E-n is self-dual up to a shift; however, that does not fully take into account the action of the automorphism group G(n) of the formal group in question. In this paper we find that the G(...
