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作者：Frisch, Joshua; Tamuz, Omer; Ferdowsi, Pooya Vahidi
作者单位：California Institute of Technology
摘要：A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.
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作者：Bitoun, Thomas
作者单位：University of Oxford
摘要：For a smooth variety Y over a perfect field of positive characteristic, the sheaf DY of crystalline differential operators on Y (also called the sheaf of PD-differential operators) is known to be an Azumaya algebra over TY, the cotangent space of the Frobenius twist Y of Y. Thus to a sheaf of modules M over DY one can assign a closed subvariety of TY, called the p-support, namely the support of M seen as a sheaf on TY. We study here the family of p-supports assigned to the reductions modulo pr...
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作者：Shokrieh, Farbod; Wu, Chenxi
作者单位：Cornell University; Rutgers University System; Rutgers University New Brunswick
摘要：We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of hyperbolic measures on universal covers of metric graphs. Kazhdan's theorem for Riemann surfaces describes the limiting behavior of canonical (Arakelov) measures on finite covers in relation to the hyperbolic measure. We will prove a generalized version of this theorem for metric graphs, allowing any infinite Galois cover to replace the universal cover. We will sh...
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作者：Aprodu, Marian; Farkas, Gavril; Papadima, Stefan; Raicu, Claudiu; Weyman, Jerzy
作者单位：Institute of Mathematics of the Romanian Academy; University of Bucharest; Humboldt University of Berlin; University of Notre Dame; University of Connecticut; Jagiellonian University
摘要：We prove a strong vanishing result for finite length Koszul modules, and use it to derive Green's conjecture for every g-cuspidal rational curve over an algebraically closed field documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbf {k}}}$$\end{document}, with char(k)=0\documentclass[12pt]{minimal} \usepackage{...
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作者：Garcia, Luis E.; Sankaran, Siddarth
作者单位：University of Toronto; University of Manitoba
摘要：We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conjecture put forward by Kudla relates these derivatives to arithmetic intersections of special cycles, and our results settle the part of his conjecture involving local archimedean...
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作者：Hop Dang Nguyen; Ngo Viet Trung
作者单位：Vietnam Academy of Science & Technology (VAST); Vietnam Academy of Science & Technology (VAST)
摘要：This paper addresses the problem of comparing minimal free resolutions of symbolic powers of an ideal. Our investigation is focused on the behavior of the function depthR/I(t)=dimR-pdI(t)-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{depth}\,}}R/I{(t)} = \dim R -{{\,\mathrm{pd}\,}}I{(t)} - 1$$\end{do...
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作者：Cohn, Henry; Goncalves, Felipe
作者单位：Microsoft; University of Alberta; University of Bonn
摘要：We prove an optimal bound in twelve dimensions for the uncertainty principle of Bourgain, Clozel, and Kahane. Suppose f : R-12 -> R is an integrable function that is not identically zero. Normalize its Fourier transform (f) over cap by (f) over cap(xi) = integral(Rd) f(x)e(-2 pi i < x,xi >) dx, and suppose (f) over cap is real-valued and integrable. We show that if f (0) <= 0, (f) over cap (0) <= 0, f (x) = 0 for vertical bar x vertical bar >= r(1), and (f) over cap(xi) = 0 for vertical bar xi...
