Inventiones mathematicae

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• Berkovich Spaces on Z: local study AI翻译
  作者：Poineau, Jerome
• Motivic degree zero Donaldson-Thomas invariants AI翻译
  作者：Behrend, Kai; Bryan, Jim; Szendroi, Balazs
  作者单位：University of British Columbia; University of Oxford
  摘要：Given a smooth complex threefold X, we define the virtual motive of the Hilbert scheme of n points on X. In the case when X is Calabi-Yau, gives a motivic refinement of the n-point degree zero Donaldson-Thomas invariant of X. The key example is X=a,(3), where the Hilbert scheme can be expressed as the critical locus of a regular function on a smooth variety, and its virtual motive is defined in terms of the Denef-Loeser motivic nearby fiber. A crucial technical result asserts that if a functio...
• Banach-valued holomorphic functions on the maximal ideal space of H∞ AI翻译
  作者：Brudnyi, Alexander
  作者单位：University of Calgary
  摘要：We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H (a) of bounded holomorphic functions on the unit disk with pointwise multiplication and supremum norm. In particular, we establish vanishing cohomology for sheaves of germs of such functions and, solving a Banach-valued corona problem for H (a), prove that the maximal ideal space of the algebra of holomorphic functions on with relatively compact images in a commutative unital...
• The index of an algebraic variety AI翻译
  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...
• Integrable measure equivalence and rigidity of hyperbolic lattices AI翻译
  作者：Bader, Uri; Furman, Alex; Sauer, Roman
  作者单位：Technion Israel Institute of Technology; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Chicago
  摘要：We study rigidity properties of lattices in , na parts per thousand yen3, and of surface groups in in the context of integrable measure equivalence. The results for lattices in , na parts per thousand yen3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the lack of Mostow rigidity for n=2 we show that cocompact lattices in allow a similar integrable measure equivalence classification.
• Image of I⟩-adic Galois representations modulo p AI翻译
  作者：Hida, Haruzo
  作者单位：University of California System; University of California Los Angeles
  摘要：Let pa parts per thousand yen5 be a prime. If an irreducible component of the spectrum of the 'big' ordinary Hecke algebra does not have complex multiplication, under mild assumptions, we prove that the image of its mod p Galois representation contains an open subgroup of for the canonical weight variable T. This fact appears to be deep, as it is almost equivalent to the vanishing of the mu-invariant of the Kubota-Leopoldt p-adic L-function and the anticyclotomic Katz p-adic L-function. Anothe...
• The Langlands-Kottwitz approach for some simple Shimura varieties AI翻译
  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.
• Suita conjecture and the Ohsawa-Takegoshi extension theorem AI翻译
  作者：Blocki, Zbigniew
  作者单位：Jagiellonian University
  摘要：We prove a conjecture of N. Suita which says that for any bounded domain D in a, one has , where c (D) (z) is the logarithmic capacity of a,a-D with respect to zaD and K (D) the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.
• Tensor tomography on surfaces AI翻译
  作者：Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
  作者单位：University of Cambridge; University of Jyvaskyla; University of Washington; University of Washington Seattle; University of California System; University of California Irvine
  摘要：We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.
• Local models of Shimura varieties and a conjecture of Kottwitz AI翻译
  作者：Pappas, G.; Zhu, X.
  作者单位：Michigan State University; Northwestern University
  摘要：We give a group theoretic definition of local models as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a p-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixe...