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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：Krishna, Amalendu
作者单位：Tata Institute of Fundamental Research (TIFR)
摘要：We show that the Levine-Weibel Chow group of 0-cycles CHd(A) of a reduced affine algebra A of dimension d >= 2 over an algebraically closed field is torsion-free. Among several applications, it implies an affirmative solution to an old conjecture of Murthy in classical K-theory.
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作者：Bamler, Richard H.; Cabezas-Rivas, Esther; Wilking, Burkhard
作者单位：University of California System; University of California Berkeley; Goethe University Frankfurt; University of Munster
摘要：We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that metrics whose curvature operator has eigenvalues greater than -1 can be evolved by the Ricci flow for some uniform time such that the eigenvalues of the curvature operator remain greater than -C. Here the time of existence and the constant C only depend on t...
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作者：Li, Yang
作者单位：Imperial College London
摘要：Motivated by the study of collapsing Calabi-Yau 3-folds with a Lefschetz K3 fibration, we construct a complete Calabi-Yau metric on C3 with maximal volume growth, which in the appropriate scale is expected to model the collapsing metric near the nodal point. This new Calabi-Yau metric has singular tangent cone at infinity C2/Z2xC, and its Riemannian geometry has certain non-standard features near the singularity of the tangent cone, which are more typical of adiabatic limit problems. The proof...
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作者：Zhou, Xin; Zhu, Jonathan J.
作者单位：University of California System; University of California Santa Barbara; Harvard University; Princeton University
摘要：In this paper, we develop a min-max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a corollary, we prove the existence of a nontrivial, smooth, closed, almost embedded, CMC hypersurface of any given mean curvature c. Moreover, if c is nonzero then our min-max solution always has multiplicity one.
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作者：Nicaise, Johannes; Shinder, Evgeny
作者单位：Imperial College London; KU Leuven; University of Sheffield; HSE University (National Research University Higher School of Economics)
摘要：We prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities. Our proof is based on motivic specialization techniques and the criterion of Larsen and Lunts for stable rationality in the Grothendieck ring of varieties.
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作者：Salter, Nick
作者单位：Columbia University
摘要：Given an ample line bundle on a toric surface, a question of Donaldson asks which simple closed curves can be vanishing cycles for nodal degenerations of smooth curves in the complete linear system. This paper provides a complete answer. This is accomplished by reformulating the problem in terms of the mapping class group-valued monodromy of the linear system, and giving a precise determination of this monodromy group.
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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...
