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作者：Hamann, Linus; Hansen, David; Scholze, Peter
作者单位：Harvard University; National University of Singapore; Max Planck Society
摘要：We develop the theory of geometric Eisenstein series and constant term functors for & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ell $\end{document}-adic sheaves on stacks of bundles on the Fargues-Fontaine curve. In particular, we prove essentially optimal finiteness theorems for these functors, analogous...
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作者：Matomaki, Kaisa; Radziwill, Maksym; Shao, Xuancheng; Tao, Terence; Teravainen, Joni
作者单位：University of Turku; Northwestern University; University of Kentucky; University of California System; University of California Los Angeles; University of Cambridge
摘要：We study higher uniformity properties of the von Mangoldt function Lambda, the M & ouml;bius function mu, and the divisor functions d(k) on short intervals(x, x+H]for almost all x is an element of[X,2X].Let Lambda(& sharp;)and d(k)(& sharp;)be suitable approximants of Lambda and d(k) ,G/ Gamma a filtered nilmanifold, and F:G/ Gamma ->& Copf;a Lipschitz function. Then our results imply for instance that when X1/3+epsilon <= H <= Xwe have, for almost all x is an element of[X,2X], sup(g is an ele...
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作者：Jian, Wangjian; Song, Jian; Tian, Gang
作者单位：Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Rutgers University System; Rutgers University New Brunswick; Peking University; Peking University
摘要：We establish the scalar curvature and distance bounds, extending Perelman's work on the Fano K & auml;hler-Ricci flow to general finite time solutions of the K & auml;hler-Ricci flow. These bounds are achieved by our Li-Yau type and Harnack estimates for weighted Ricci potential functions of the K & auml;hler-Ricci flow. We further prove that the Type I blow-ups of the finite time solution always sub-converge in Gromov-Hausdorff sense to an ancient solution on a family of analytic normal varie...
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作者：Bishop, Christopher J.; Rempe, Lasse
作者单位：State University of New York (SUNY) System; Stony Brook University; University of Manchester
摘要：We show that every open Riemann surface X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely many triangles. Equivalently, X\documentclass[12pt]{minimal} \usepackage{a...
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作者：Toma, Radu
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：Let N be a prime and phi be a Hecke-Maa ss cuspidal newform for the Hecke congruence subgroup Gamma 0(N) in SLn(R). We define a notion of the bulk Omega N of the space Gamma 0(N)\SLn(R)/SO(n) with respect to a compact set Omega subset of SLn(R). For any prime n, we prove sub-baseline bounds for the sup-norm of phi restricted to Omega N. Conditionally on GRH, we generalise this result to all n >= 2. The methods involve a new reduction theory with level structure, based on generalisations of Atk...
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作者：Cautis, Sabin; Williams, Harold
作者单位：University of British Columbia; University of Southern California
摘要：We construct and study a nonstandard t-structure on the derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima space of triples R-G,R-N, where N is a representation of a reductive group G. Its heart KPG,N is a finite-length, rigid, monoidal abelian category with renormalized r-matrices. We refer to objects of KPG,N as Koszul-perverse coherent sheaves. Simple objects of KPG,N define a canonical basis in the quantized K-theoretic Coulomb branch of the associated ga...
