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作者：Liu, Bo; Ma, Xiaonan
作者单位：East China Normal University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：In this paper we obtain a localization formula in differential K-theory for S-1-actions. We establish a localization formula for equivariant eta-invariants by combining this result with our extension of Goette's result on the comparison of two types of equivariant eta-invariants. An important step in our approach is to construct a pre-lambda-ring structure in differential K-theory.
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作者：Atobe, Hiraku
作者单位：Hokkaido University
摘要：In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them in terms of linear combinations of standard modules with rational coefficients. The main ingredient of this computation is to apply M oe glin's explicit construction of local A-packets to tempered L-packets. Finally, we study the derivatives introduced by M...
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作者：Nachman, Adrian; Regev, Idan; Tataru, Daniel
作者单位：University of Toronto; University of California System; University of California Berkeley
摘要：We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in L2 for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calderon in dimension 2, for conductivities sigma>0 with log sigma is an element of H1. The proof of the nonlinear Plancherel theorem includes...
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作者：Efimov, Alexander, I
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)
摘要：We disprove two (unpublished) conjectures of Kontsevich which state generalized versions of categorical Hodge-to-de Rham degeneration for smooth and for proper DG categories (but not smooth and proper, in which case degeneration is proved by Kaledin (in: Algebra, geometry, and physics in the 21st century. Birkhauser/Springer, Cham, pp 99-129, 2017). In particular, we show that there exists a minimal 10-dimensional A infinity-algebra over a field of characteristic zero, for which the supertrace...
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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：Burungale, Ashay A.; Tian, Ye
作者单位：California Institute of Technology; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Chinese Academy of Sciences
摘要：Let E be a CM elliptic curve over the rationals and p>3-Selmer group Selp infinity(E/Q) and the complex L-function L(s,E/Q). In particular, the Tate-Shafarevich group X(E/Q) is finite whenever corankZpSelp infinity(E/Q)=1. We also prove an analogous p-converse for CM abelian varieties arising from weight two elliptic CM modular forms with trivial central character. For non-CM elliptic curves over the rationals, first general results towards such a p-converse theorem are independently due to Sk...
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作者：Good, Chris; Meddaugh, Jonathan
作者单位：University of Birmingham; Baylor University
摘要：Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let X be a compact totally disconnected space and f:X -> X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69p...
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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 ...
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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 ...
