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作者：Asok, Aravind; Fasel, Jean; Williams, Ben
作者单位：University of Southern California; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of British Columbia
摘要：We show that an old conjecture of A. A. Suslin characterizing the image of a Hurewicz map from Quillen K-theory in degree n to Milnor K-theory in degree n admits an interpretation in terms of unstable A1-homotopy sheaves of the general linear group. Using this identification, we establish Suslin's conjecture in degree 5 for infinite fields having characteristic unequal to 2 or 3. We do this by linking the relevant unstable A1-homotopy sheaf of the general linear group to the stable A1-homotopy...
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作者：Chambers, Gregory R.; Liokumovich, Yevgeny
作者单位：Rice University; Massachusetts Institute of Technology (MIT); University of Toronto
摘要：We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region U can be swept out by a family of hypersurfaces of volume at most V, then it can be swept out by a family of mutually disjoint hypersurfaces of volume at most V+epsilon.
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作者：Killip, Rowan; Murphy, Jason; Visan, Monica
作者单位：University of California System; University of California Los Angeles; University of Missouri System; Missouri University of Science & Technology
摘要：We consider the Korteweg-de Vries equation with white noise initial data, posed on the whole real line, and prove the almost sure existence of solutions. Moreover, we show that the solutions obey the group property and follow a white noise law at all times, past or future. As an offshoot of our methods, we also obtain a new proof of the existence of solutions and the invariance of white noise measure in the torus setting.
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作者：Benoist, Olivier; Wittenberg, Olivier
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We formulate the real integral Hodge conjecture, a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel-Haefliger cycle class map for 1-cycles, with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of co...
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作者：Hesselholt, Lars; Larsen, Michael; Lindenstrauss, Ayelet
作者单位：Nagoya University; University of Copenhagen; Indiana University System; Indiana University Bloomington
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作者：Chen, Dawei; Moeller, Martin; Sauvaget, Adrien; Zagier, Don
作者单位：Boston College; Goethe University Frankfurt; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite
摘要：We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained using intersection theory on strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel-Veech constants for all strata. We also show that the same results hold for the spin and hyperelliptic components of the strata.
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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：Andre, Y.; Corvaja, P.; Zannier, U.
作者单位：Sorbonne Universite; Universite Paris Cite; University of Udine; Scuola Normale Superiore di Pisa
摘要：Given a point. on a complex abelian variety A, its abelian logarithm can be expressed as a linear combination of the periods of A with real coefficients, the Betti coordinates of.. When ( A,.) varies in an algebraic family, these coordinates define a system of multivalued real-analytic functions. Computing its rank (in the sense of differential geometry) becomes important when one is interested about how often. takes a torsion value (for instance, Manin's theorem of the kernel implies that thi...
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作者：Bullett, Shaun; Lomonaco, Luna
作者单位：University of London; Queen Mary University London; Universidade de Sao Paulo
摘要：In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of (2 : 2) holomorphic correspondences Fa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {F}_a$$\end{document} the correspondence Fa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \us...
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作者：Figalli, Alessio; Serra, Joaquim
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that every bounded stable solution of (-Delta)1/2u+f(u)=0 in R3 is a 1D profile, i.e., u(x)=phi(e center dot x) for some e is an element of S2, where phi:R -> R is a nondecreasing bounded stable solution in dimension one. Equivalently, stable critical points of boundary reaction problems in R+d+1=Rd+1 boolean AND{xd+1 >= 0} of the form {xd+1 >= 0}12| are 1D when d=3 These equations have been studied since the 1940's in crystal dislocations. Also, as it happens for the Allen-Cahn equat...
