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作者：Krah, Johannes
作者单位：University of Bielefeld
摘要：We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.
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作者：Chow, Sam; Yang, Lei
作者单位：University of Warwick; Institute for Advanced Study - USA
摘要：Given any line in the plane, we strengthen the Littlewood conjecture by two logarithms for almost every point on the line, thereby generalising the fibre result of Beresnevich, Haynes, and Velani. To achieve this, we prove an effective asymptotic equidistribution result for one-parameter unipotent orbits in SL(3, R)/SL(3, Z). We also provide a complementary convergence statement, by developing the structural theory of dual Bohr sets: at the cost of a slightly stronger Diophantine assumption, t...
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作者：Iyengar, Srikanth B.; Khare, Chandrashekhar B.; Manning, Jeffrey
作者单位：Utah System of Higher Education; University of Utah; University of California System; University of California Los Angeles
摘要：We define a congruence module Psi(A)(M) associated to a surjective O\-algebra morphism lambda:A -> O, with O a discrete valuation ring, A a complete noetherian local O-algebra regular at p, the kernel of lambda, and M a finitely generated A-module. We establish a numerical criterion for M to have a free direct summand over A of positive rank. It is in terms of the lengths of Psi(A)(M) and the torsion part of p/p(2). It generalizes results of Wiles, Lenstra, and Diamond, that deal with the case...
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作者：Huang, Jingyin
作者单位：University System of Ohio; Ohio State University
摘要：We show that for a large class of Artin groups with Dynkin diagrams being a tree, the K(pi,1)-conjecture holds. We also establish the K(pi,1)-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which applies to some hyperbolic type Artin groups. This is based on a new approach to the K(pi,1)-conjecture for Artin groups.
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作者：De Roeck, Wojciech; Elgart, Alexander; Fraas, Martin
作者单位：KU Leuven; Virginia Polytechnic Institute & State University
摘要：This work justifies the linear response formula for the Hall conductance of a two-dimensional disordered system. The proof rests on controlling the dynamics associated with a random time-dependent Hamiltonian. The principal challenge is related to the fact that spectral and dynamical localization are intrinsically unstable under perturbation, and the exact spectral flow - the tool used previously to control the dynamics in this context - does not exist. We resolve this problem by proving a loc...
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作者：Ji, Ran; Wu, Yunhui
作者单位：Tsinghua University; Capital Normal University; Tsinghua University
摘要：In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M$\end{document} of finite volume with sectional curvature -1 <= K <= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...
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作者：Karpukhin, Mikhail; Stern, Daniel
作者单位：California Institute of Technology; University of Chicago
摘要：We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold (M-n,g) of dimension n>2 to any closed, non-aspherical manifold N containing no stable minimal two-spheres. In particular, this gives the first general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets. In the special case of the round spheres N=S-k, k >= 3, we obtain a distinguished family of nonconstant harmonic maps M ->...
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作者：Killip, Rowan; Laurens, Thierry; Visan, Monica
作者单位：University of California System; University of California Los Angeles; University of Wisconsin System; University of Wisconsin Madison
摘要：The Benjamin-Ono equation is shown to be well-posed, both on the line and on the circle, in the Sobolev spaces H(s )for s>-(1)|(2). The proof rests on a new gauge transfor-mation and benefits from our introduction of a modified Lax pair representation of the full hierarchy. As we will show, these developments yield important additional divi-dends beyond well-posedness, including (i) the unification of the diverse approaches to polynomial conservation laws; (ii) a generalization of G & eacute;r...
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作者：Baldi, Gregorio; Klingler, Bruno; Ullmo, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Humboldt University of Berlin
摘要：Given a polarizable Z-variation of Hodge structures V over a complex smooth quasi-projective base S, a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus where exceptional Hodge tensors appear) is a countable union of irreducible algebraic subvarieties of S, called the special subvarieties for V. Our main result in this paper is that, if the level of V is at least 3, this Hodge locus is in fact a finite union of such special subvarieties (hence is algebra...
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作者：Sawin, Will; Wood, Melanie Matchett
作者单位：Princeton University; Harvard University
摘要：For G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} and H1,& mldr;,Hn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H...
