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作者：Horbez, Camille
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Let G=G1 & lowast;& mldr;& lowast;Gk & lowast;F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G=G_{1}\ast \dots \ast G_{k}\ast F$\end{document} be a countable group which splits as a free product, where all groups Gi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa...
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作者：Kurlberg, Par; Lester, Stephen
作者单位：Royal Institute of Technology; University of London; King's College London
摘要：We show that along a density one subsequence of admissible radii, the nearest neighbor spacing between lattice points on circles is Poissonian.
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作者：Geng, Jun; Shen, Zhongwei
作者单位：Lanzhou University; Westlake University
摘要：We establish resolvent estimates in spaces of bounded solenoidal functions for the Stokes operator in a bounded domain Omega in Rd under the assumptions that Omega is C1 for d >= 3 and Lipschitz for d=2. As a corollary, it follows that the Stokes operator generates a uniformly bounded analytic semigroup in the spaces of bounded solenoidal functions in Omega. The smoothness conditions on Omega are sharp. The case of exterior domains with nonsmooth boundaries is also studied. The key step in our...
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作者：Heuer, Ben
作者单位：Goethe University Frankfurt
摘要：For any smooth proper rigid analytic space X over a complete algebraically closed extension of Qp, we construct a p-adic Simpson correspondence: an equivalence of categories between vector bundles on Scholze's pro-etale site of X and Higgs bundles on X. This generalises a result of Faltings from smooth projective curves to any higher dimension, and further to the rigid analytic setup. The strategy is new, and is based on the study of rigid analytic moduli spaces of pro-etale invertible sheaves...
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作者：Yang, Enlin; Zhao, Yigeng
作者单位：Peking University; Westlake University
摘要：We confirm the quasi-projective case of Saito's conjecture (Invent. Math. 207:597-695, 2017), namely that the cohomological characteristic classes defined by Abbes and Saito can be computed in terms of the characteristic cycles. We construct a cohomological characteristic class supported on the non-acyclicity locus of a separated morphism relatively to a constructible sheaf. As applications of the functorial properties of this class, we prove cohomological analogs of the Milnor formula and the...
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作者：Crowley, Diarmuid; Goette, Sebastian; Nordstrom, Johannes
作者单位：University of Melbourne; University of Freiburg; University of Bath
摘要：We prove that the moduli space of holonomy G2-metrics on a closed 7-manifold can be disconnected by presenting a number of explicit examples. We detect different connected components of the G2-moduli space by defining an analytic refinement nu(M, g). Z of the defect invariant nu(M,phi)is an element of Z/48-structures. on a closed 7-manifold M introduced by the first and third authors. The nu-invariant is defined using.-invariants and Mathai-Quillen currents on M and we compute it for twisted c...
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作者：Kartal, Yusuf Baris
作者单位：University of Edinburgh
摘要：Inspired by the work of Bell on the dynamical Mordell-Lang conjecture, and by family Floer cohomology, we construct p-adic analytic families of bimodules on the Fukaya category of a monotone or negatively monotone symplectic manifold, interpolating the bimodules corresponding to iterates of a symplectomorphism f isotopic to the identity. This family can be thought of as a p-adic analytic action on the Fukaya category. Using this, we deduce that the ranks of the Floer cohomology groups HF(phi k...
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作者：Li, Chi; Zhou, Zhengyi
作者单位：Rutgers University System; Rutgers University New Brunswick; Chinese Academy of Sciences; Chinese Academy of Sciences; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：Let X be a smooth complex manifold. Assume that Y subset of X is a K & auml;hler submanifold such that X\Y is biholomorphic to Cn. We prove that (X,Y) is biholomorphic to (Pn,Pn-1). We then study certain K & auml;hler orbifold compactifications of Cn and, as an application, prove that on C3 the flat metric is the only asymptotically conical Ricci-flat K & auml;hler metric whose metric cone at infinity has a smooth link. As a key technical ingredient, we derive a new characterization of minimal...
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作者：Fleschler, Ian; Tolsa, Xavier; Villa, Michele
作者单位：Princeton University; ICREA; Autonomous University of Barcelona; Centre de Recerca Matematica (CRM); University of Oulu; University of Basque Country
摘要：In this paper we prove a higher dimensional analogue of Carleson's epsilon 2 conjecture. Given two arbitrary disjoint Borel sets Omega(+),Omega(-)subset of Rn+1, and x is an element of Rn+1, r>0, we denote epsilon(n)(x,r):=1/r(n) inf(H+)H(n)(((partial derivative B(x,r)boolean AND H+)\Omega(+))boolean OR((partial derivative B(x,r)boolean AND H-)\Omega(-))), where the infimum is taken over all open affine half-spaces H+ such that x is an element of partial derivative H+ and we define H-=Rn+1\H+....
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作者：Kuznetsov, Alexander; Shinder, Evgeny
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; HSE University (National Research University Higher School of Economics); University of Sheffield; University of Bonn
摘要：Using the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree d is an element of{2,3,4,5}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d \in \{2,3,4,5\}$\end{document} and crepant categorical resolutions of the non...
