Inventiones mathematicae

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• Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones AI翻译
  作者：Chen, Xuemiao; Sun, Song
  作者单位：University System of Maryland; University of Maryland College Park; University of California System; University of California Berkeley
  摘要：In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian-Yang-Mills connections over any reflexive sheaves.
• Exponential decay of correlations in the two-dimensional random field Ising model AI翻译
  作者：Ding, Jian; Xia, Jiaming
  作者单位：University of Pennsylvania
  摘要：We study the random field Ising model on Z(2) where the external field is given by i.i.d. Gaussian variables with mean zero and positive variance. We show that the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary.
• Nuclear dimension of simple C*-algebras AI翻译
  作者：Castillejos, Jorge; Evington, Samuel; Tikuisis, Aaron; White, Stuart; Winter, Wilhelm
  作者单位：KU Leuven; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Oxford; University of Ottawa; University of Glasgow; University of Munster
  摘要：We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large classes of C*-algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.
• Higher Eisenstein elements, higher Eichler formulas and rank of Hecke algebras AI翻译
  作者：Lecouturier, Emmanuel
  作者单位：Tsinghua University
  摘要：Let N and p be primes such that p divides the numerator of N-1/12. In this paper, we study the rank g(p) of the completion of the Hecke algebra acting on cuspidal modular forms of weight 2 and level Gamma(0)(N) at the p-maximal Eisenstein ideal. We give in particular an explicit criterion to know if g(p) >= 3, thus answering partially a question of Mazur. In order to study g(p), we develop the theory of higher Eisenstein elements, and compute the first few such elements in four different Hecke...
• Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution AI翻译
  作者：Hermon, Jonathan; Hutchcroft, Tom
  作者单位：University of British Columbia; University of Cambridge
  摘要：Let G be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. We prove that if G is nonamenable and p > p(c)(G) then there exists a positive constant c(p) such that P-p(n <= vertical bar K vertical bar < infinity) <= e(-cpn) for every n >= 1, where K is the cluster of the origin. We deduce the following two corollaries: 1. Every infinite cluster in supercritical percolation on a transitive non-amenable graph has anchored expansion almost surely. This ans...
• Standard conjectures for abelian fourfolds AI翻译
  作者：Ancona, Giuseppe
  作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
  摘要：Let A be an abelian fourfold in characteristic p. We prove the standard conjecture of Hodge type for A, namely that the intersection product Z(num)(2)(A)(Q) x Z(num)(2) (A)(Q) -> Q is of signature (rho(2) - rho(1) + 1; rho(1) - 1), with rho(n) = dim Z(num)(n)(A)(Q). (Equivalently, it is positive definite when restricted to primitive classes for any choice of the polarization.) The approach consists in reformulating this question into a p-adic problem and then using p-adic Hodge theory to solve...
• CM values of higher automorphic Green functions for orthogonal groups AI翻译
  作者：Bruinier, Jan Hendrik; Ehlen, Stephan; Yang, Tonghai
  作者单位：Technical University of Darmstadt; University of Cologne; University of Wisconsin System; University of Wisconsin Madison
  摘要：Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function G(s) (z(1), z(2)) for the elliptic modular group at positive integral spectral parameter s are given by logarithms of algebraic numbers in suitable class fields. We prove a partial average version of this conjecture, where we sum in the first variable z(1) over all CM points of a fixed discriminant d(1) (twisted by a genus character), and allow in the second variable the evaluation a...
• Regularity of the free boundary for the two-phase Bernoulli problem AI翻译
  作者：De Philippis, Guido; Spolaor, Luca; Velichkov, Bozhidar
  作者单位：New York University; University of California System; University of California San Diego; University of Pisa
  摘要：We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.
• Dynamical uniform boundedness and the abc-conjecture AI翻译
  作者：Looper, Nicole R.
  作者单位：Brown University
  摘要：We address the Uniform Boundedness Conjecture of Morton and Silverman in the case of unicritical polynomials, assuming a generalization of the abc-conjecture. For unicritical polynomials of degree at least five, we require only the standard abc-conjecture.
• Positivity of the CM line bundle for families of K-stable klt Fano varieties AI翻译
  作者：Codogni, Giulio; Patakfalvi, Zsolt
  作者单位：University of Rome Tor Vergata; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
  摘要：The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle boils down to showing semi-positivity/positivity statements about the CM-line bundle for families with K-semi-stable/K-polystable fibers. We prove the necessary semi-positivity statements in the K-semi-stable situation, and the necessary posi...