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作者：Eichmair, Michael; Metzger, Jan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Potsdam
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作者：White, Brian
作者单位：Stanford University
摘要：Consider the mean curvature flow of an (n+1)-dimensional compact, mean convex region in Euclidean space (or, if n < 7, in a Riemannian manifold). We prove that elements of the mth homotopy group of the complementary region can die only if there is a shrinking S (k) xR (n-k) singularity for some ka parts per thousand currency signm. We also prove that for each m with 1a parts per thousand currency signma parts per thousand currency signn, there is a nonempty open set of compact, mean convex reg...
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作者：Kobayashi, Shinichi
作者单位：Tohoku University
摘要：Let p be a prime number and let E be an elliptic curve defined over ae of conductor N. Let K be an imaginary quadratic field with discriminant prime to pN such that all prime factors of N split in K. B. Perrin-Riou established the p-adic Gross-Zagier formula that relates the first derivative of the p-adic L-function of E over K to the p-adic height of the Heegner point for K when E has good ordinary reduction at p. In this article, we prove the p-adic Gross-Zagier formula of E for the cyclotom...
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作者：Poineau, Jerome
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作者：Gabber, Ofer; Liu, Qing; Lorenzini, Dino
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; University System of Georgia; University of Georgia
摘要：Let K be the field of fractions of a Henselian discrete valuation ring . Let X (K) /K be a smooth proper geometrically connected scheme admitting a regular model . We show that the index delta(X (K) /K) of X (K) /K can be explicitly computed using data pertaining only to the special fiber X (k) /k of the model X. We give two proofs of this theorem, using two moving lemmas. One moving lemma pertains to horizontal 1-cycles on a regular projective scheme X over the spectrum of a semi-local Dedeki...
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作者：Scholze, Peter
作者单位：University of Bonn
摘要：We show how the Langlands-Kottwitz method can be used to determine the semisimple local factors of the Hasse-Weil zeta-function of certain Shimura varieties. This is made possible by a new result describing part of the nearby cycle sheaves in certain situations. In combination with a general base-change lemma in harmonic analysis, we use this to prove a conjecture of Haines and Kottwitz for these Shimura varieties.
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作者：Alper, Jarod; Fedorchuk, Maksym; Smyth, David Ishii
作者单位：Universidad de los Andes (Colombia); Columbia University; Harvard University
摘要：We prove that a generic canonically or bicanonically embedded smooth curve has semistable mth Hilbert points for all ma parts per thousand yen2. We also prove that a generic bicanonically embedded smooth curve has stable mth Hilbert points for all ma parts per thousand yen3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with -action, namely the canonically embedded balanced ribbon and the canonically embedded balanced double A (2...
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作者：Hartl, Urs
作者单位：University of Munster
摘要：In their book, Rapoport and Zink constructed rigid analytic period spaces for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of p-divisible groups to some of these period spaces. They conjectured the existence of an ,tale bijective morphism of rigid analytic spaces and of a universal local system of ae (p) -vector spaces on . Such a local system would give rise to a tower of ,tale covering spaces of , equipped with a Hecke-action, and an action of the automorphism...
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作者：Blomer, Valentin
摘要：We develop a fairly explicit Kuznetsov formula on GL(3) and discuss the analytic behavior of the test functions on both sides. Applications to Weyl's law, exceptional eigenvalues, a large sieve and L-functions are given.
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作者：de Fernex, Tommaso
作者单位：Utah System of Higher Education; University of Utah
摘要：We prove that for Na parts per thousand yen4, all smooth hypersurfaces of degree N in a(TM) (N) are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals.
