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作者：He, Qiao; Li, Chao; Shi, Yousheng; Yang, Tonghai
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University; Zhejiang University
摘要：We prove the Kudla-Rapoport conjecture for Kramer models of unitary Rapoport-Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kramer models and modified derived local densities of hermitian forms. As an application, we relax the local assumptions at ramified places in the arithmetic Siegel-Weil formula for unitary Shimura varieties, which is in particular applicable to unitary Shimura varieties associated to unimodular hermit...
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作者：Bright, Martin; Newton, Rachel
作者单位：University of London; King's College London
摘要：Classifying elements of the Brauer group of a variety X over a p-adic field by the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filtration to that defined by Kato's Swan conductor. The refined Swan conductor con-trols how the evaluation maps vary on p-adic discs: this provides a geometric char-acterisation of the refined Swan conductor. We give applications to rational points on varieties over number fields, including failure of weak approximation for vari...
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作者：Ivorra, Florian; Sebag, Julien
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let k be a field of characteristic zero and let X be an algebraic k-variety endowed with an action of the multiplicative algebraic monoid A(1). In this article, we prove that the nearby motivic sheaf functor of a weighted A(1)-equivariant function on X commutes with direct (and exceptional direct) images when applied to constant objects and their twists by Thom spaces of equivariant vector bundles. This proves a generalized categorified version of the conjectures of Behrend-Bryan-Szendro?i and...
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作者：Blomer, Valentin
摘要：Strong bounds-going beyond Sarnak's density hypothesis-are obtained for the number of automorphic forms for the group Gamma(0)(q) subset of SL(n, Z) violating the Ramanujan conjecture at any given unramified place. The proof is based on a relative trace formula of Kuznetsov type and best-possible bounds for certain Kloosterman sums for GL(n). Further applications are given.
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作者：Pstragowski, Piotr
作者单位：Harvard University
摘要：To an Adams-type homology theory we associate the notion of a synthetic spectrum; this is a product-preserving sheaf on the site of finite spectra with projective E-homology. We show that the infinity-category SynE of synthetic spectra based on E is in a precise sense a deformation of the infinity-category of spectra into quasi-coherent sheaves over a certain algebraic stack, and show that this deformation encodes the E*-based Adams spectral sequence. We describe a symmetric monoidal functor f...
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作者：Kozlowski, Karol K.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Claude Bernard Lyon 1; Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：This paper develops a technique allowing one to prove the convergence of a class of series of multiple integrals which corresponds to the form factor expansion of space-like separated two-point functions in the 1+1 dimensional massive integrable Sinh-Gordon quantum field theory.
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作者：Fehrman, Benjamin; Gess, Benjamin
作者单位：University of Oxford; University of Bielefeld; Max Planck Society
摘要：Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate parabolic-hyperbolic PDE with irregular drift. We develop a robust well-posedness theory for such PDEs in energy critical spaces based on concepts of renormalized solutions and the equation's kinetic form. We establish these properties by proving that renormalized solutions a...
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作者：Belov, Yurii; Kulikov, Aleksei; Lyubarskii, Yurii
作者单位：Norwegian University of Science & Technology (NTNU)
摘要：We study the frame properties of the Gabor systems G(g; alpha, beta) := {e(2 pi i beta mx) g(x - an)} m,n is an element of Z. In particular, we prove that forHerglotzwindows g such systems always form a frame for L-2(R) if alpha, beta > 0, alpha beta <= 1. For general rationalwindows g is an element of L-2(R) we prove that G(g; alpha, beta) is a frame for L-2(R) if 0 < alpha, beta, alpha beta < 1, alpha beta is not an element of Q and (g) over bar(xi) not equal 0, xi > 0, thus confirming Daube...
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作者：Skorobogatov, Alexei N.; Sofos, Efthymios
作者单位：Imperial College London; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; University of Glasgow
摘要：We resolve Schinzel's Hypothesis (H) for 100% of polynomials of arbitrary degrees. We deduce that a positive proportion of diagonal conic bundles over Q with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Chatelet equations.
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作者：De Simoi, Jacopo; Kaloshin, Vadim; Leguil, Martin
作者单位：University of Toronto; Institute of Science & Technology - Austria; Universite de Picardie Jules Verne (UPJV); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.
