2020

最新文章

• On Kronecker terms over global function fields AI翻译
  作者：Wei, Fu-Tsun
  作者单位：National Tsing Hua University
  摘要：We establish a general Kronecker limit formula of arbitrary rank over global function fields with Drinfeld period domains playing the role of upper-half plane. The Drinfeld-Siegel units come up as equal characteristic modular forms replacing the classical Delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ...
• Chromatic homotopy theory is asymptotically algebraic AI翻译
  作者：Barthel, Tobias; Schlank, Tomer; Stapleton, Nathaniel
  作者单位：Max Planck Society; Hebrew University of Jerusalem; University of Kentucky
  摘要：Inspired by the Ax-Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects. We employ this theory to give an asymptotic solution to the approximation problem in chromatic homotopy theory. More precisely, we show that the ultraproduct of the E(n, p)-local categories over any non-principal ultrafilter on the set of prime numbers is equivalent to the ultraproduct of certain algebraic categories ...
• Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature AI翻译
  作者：Agostiniani, Virginia; Fogagnolo, Mattia; Mazzieri, Lorenzo
  作者单位：University of Verona; University of Trento
  摘要：In this paper we consider complete noncompact Riemannian manifolds (M, g) with nonnegative Ricci curvature and Euclidean volume growth, of dimension n >= 3. For every bounded open subset Omega subset of M with smooth boundary, we prove that integral(partial derivative Omega)vertical bar H/n-1 vertical bar(n-1) d sigma >= AVR(g)vertical bar Sn-1 vertical bar, where H is the mean curvature of partial derivative Omega and AVR(g) is the asymptotic volume ratio of (M, g). Moreover, the equality hol...
• Hodge filtration, minimal exponent, and local vanishing AI翻译
  作者：Mustata, Mircea; Popa, Mihnea
  作者单位：University of Michigan System; University of Michigan; Northwestern University
  摘要：We bound the generation level of the Hodge filtration on the localization along a hypersurface in terms of its minimal exponent. As a consequence, we obtain a local vanishing theorem for sheaves of forms with log poles. These results are extended to -divisors, and are derived from a result of independent interest on the generation level of the Hodge filtration on nearby and vanishing cycles.
• A reverse Sidorenko inequality AI翻译
  作者：Sah, Ashwin; Sawhney, Mehtaab; Stoner, David; Zhao, Yufei
  作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Massachusetts Institute of Technology (MIT)
  摘要：LetHbe a graph allowing loops as well as vertex and edge weights. We prove that, for every triangle-free graphGwithout isolated vertices, the weighted number of graph homomorphismshom(G,H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hom (G, H)$$\end{document}satisfies the inequalityhom(G,H)<=& x220f;uv is an el...
• Kazhdan groups have cost 1 AI翻译
  作者：Hutchcroft, Tom; Pete, Gabor
  作者单位：University of Cambridge; Budapest University of Technology & Economics
  摘要：We prove that every countably infinite group with Kazhdan's property (T) has cost 1, answering a well-known question of Gaboriau. It remains open if they have fixed price 1.
• Singularity formation for the two-dimensional harmonic map flow into S2 AI翻译
  作者：Davila, Juan; del Pino, Manuel; Wei, Juncheng
  作者单位：Universidad de Antioquia; Universidad de Chile; University of Bath; University of British Columbia
  摘要：We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S-2, u(t) = Delta u + vertical bar del u vertical bar(2)u in Omega x (0, T) u = phi on partial derivative Omega x (0, T) u(., 0) = u(0) in Omega, where Omega is a bounded, smooth domain in R-2, u : Omega x (0, T) -> S-2, u(0) : (Omega) over bar -> S-2 is smooth, and phi = u(0)vertical bar(partial derivative Omega). Given any k points q(1), ..., q(k) in the domain, we find initial and boundary data...
• On mixing diffeomorphisms of the disc AI翻译
  作者：Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
  作者单位：University of Zurich; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Universite Paris Cite; Imperial College London; Institute for Advanced Study - USA
  摘要：We prove that a Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>k$$\end{document}, k >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{do...
• The Betti map associated to a section of an abelian scheme AI翻译
  作者：Andre, Y.; Corvaja, P.; Zannier, U.
  作者单位：Sorbonne Universite; Universite Paris Cite; University of Udine; Scuola Normale Superiore di Pisa
  摘要：Given a point. on a complex abelian variety A, its abelian logarithm can be expressed as a linear combination of the periods of A with real coefficients, the Betti coordinates of.. When ( A,.) varies in an algebraic family, these coordinates define a system of multivalued real-analytic functions. Computing its rank (in the sense of differential geometry) becomes important when one is interested about how often. takes a torsion value (for instance, Manin's theorem of the kernel implies that thi...
• Mating quadratic maps with the modular group II AI翻译
  作者：Bullett, Shaun; Lomonaco, Luna
  作者单位：University of London; Queen Mary University London; Universidade de Sao Paulo
  摘要：In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of (2 : 2) holomorphic correspondences Fa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {F}_a$$\end{document} the correspondence Fa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \us...