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作者：Blumberg, Andrew J.; Mandell, Michael A.
作者单位：University of Texas System; University of Texas Austin; Indiana University System; Indiana University Bloomington
摘要：Let p is an element of Zbe an odd prime. We prove a spectral version of Tate-Poitou duality for the algebraic K-theory spectra of number rings with p inverted. This identifies the homotopy type of the fiber of the cyclotomic trace K(OF)p perpendicular to -> TC(OF)p perpendicular to TC after taking a suitably connective cover. As an application, we identify the homotopy type at odd primes of the homotopy fiber of the cyclotomic trace for the sphere spectrum in terms of the algebraic K-theory of...
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作者：Walsh, Miguel N.
作者单位：University of Buenos Aires; University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)
摘要：We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved.
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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.
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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...
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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...
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作者：Groechenig, Michael; Wyss, Dimitri; Ziegler, Paul
作者单位：University of Toronto; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Technical University of Munich
摘要：We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for...
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作者：King, Alastair; Qiu, Yu
作者单位：University of Bath; Tsinghua University
摘要：We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case that arises from an (unpunctured) marked surface, where the exchange graph is modelled on the graph of triangulations of the marked surface, we show that the universal cover of this groupoid can be constructed using the covering graph of triangulations of the surface with extra decorations. This covering graph is a skeleton for a space of...
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作者：Greer, Francois
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：We give examples of Calabi-Yau threefolds containing Lagrangian spheres which are not vanishing cycles of nodal degenerations, answering a question of Donaldson in the negative.
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作者：Kleiner, Bruce; Lang, Urs
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The large-scale geometry of hyperbolic metric spaces exhibits many distinctive features, such as the stability of quasi-geodesics (the Morse Lemma), the visibility property, and the homeomorphism between visual boundaries induced by a quasi-isometry. We prove a number of closely analogous results for spaces of rank n >= 2 in an asymptotic sense, under some weak assumptions reminiscent of nonpositive curvature. For this purpose we replace quasi-geodesic lines with quasi-minimizing (locally fini...
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作者：Nguyen Viet Dang; Guillarmou, Colin; Riviere, Gabriel; Shen, Shu
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille; Universite Paris Cite; Sorbonne Universite
摘要：We study the twisted Ruelle zeta function.X (s) for smooth Anosov vector fields X acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove the Fried conjecture, relating Reidemeister torsion and.X (0). In higher dimensions, we show more generally that.X (0) is locally constant with respect to the vector field X under a spectral condition. As a consequence, we also show the Fried conjecture for Anosov flows near the geodesic flow on the unit tangent bundle of hyperb...
