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• Cohomological Milnor formula and Saito's conjecture on characteristic classes AI翻译
  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...
• Carleson's ε2 conjecture in higher dimensions AI翻译
  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+....
• Extensions of Schoen-Simon-Yau and Schoen-Simon theorems via iteration à la De Giorgi AI翻译
  作者：Bellettini, Costante
  作者单位：University of London; University College London
  摘要：We give an alternative proof of the Schoen-Simon-Yau curvature estimates and associated Bernstein-type theorems (Schoen et al. in Acta Math. 134:275-288, 1975), and extend the original result by including the case of 6-dimensional (stable minimal) immersions. The key step is an epsilon-regularity theorem, that assumes smallness of the scale-invariant L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepack...
• The Adams differentials on the classes hj3 AI翻译
  作者：Burklund, Robert; Xu, Zhouli
  作者单位：University of Copenhagen; University of California System; University of California Los Angeles
• W*-Superrigidity for cocycle twisted group von Neumann algebras AI翻译
  作者：Donvil, Milan; Vaes, Stefaan
  作者单位：KU Leuven
  摘要：We construct countable groups G with the following new degree of W*-superrigidity: if L(G) is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra L(Lambda), then the groups G and Lambda must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary 2-cocycle. We also give examples of II1 factors N that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twis...
• The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles AI翻译
  作者：Maulik, Davesh; Shen, Junliang; Yin, Qizheng; Zhang, Ruxuan
  作者单位：Massachusetts Institute of Technology (MIT); Yale University; Peking University; Fudan University
  摘要：We show that birational hyper-K & auml;hler varieties of K3[n]-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively hyperholomorphic bundles, following ideas of Markman. Our method also proves a stronger version of the D-equivalence conjecture for hyper-K & auml;hler varieties of K3[n]-type with Brauer classes.