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作者：Weinstein, Jared
作者单位：Boston University
摘要：We produce an integral model for the modular curve over the ring of integers of a sufficiently ramified extension of whose special fiber is a semistable curve in the sense that its only singularities are normal crossings. This is done by constructing a semistable covering (in the sense of Coleman) of the supersingular part of , which is a union of copies of a Lubin-Tate curve. In doing so we tie together non-abelian Lubin-Tate theory to the representation-theoretic point of view afforded by Bu...
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作者：Dasgupta, Samit
作者单位：University of California System; University of California Santa Cruz
摘要：We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota-Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg's exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, who proved a factorization result for the Katz p-adic L-series associated to the restriction of a Diri...
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作者：Benoist, Yves; de Saxce, Nicolas
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
摘要：We establish the spectral gap property for dense subgroups generated by algebraic elements in any compact simple Lie group, generalizing earlier results of Bourgain and Gamburd for unitary groups.
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作者：Hoering, Andreas; Peternell, Thomas
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); University of Bayreuth
摘要：Let be a compact Kahler threefold that is not uniruled. We prove that has a minimal model.
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作者：Damanik, David; Gorodetski, Anton; Yessen, William
作者单位：Rice University; University of California System; University of California Irvine
摘要：We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and establish relations between its spectrum and spectral characteristics (namely, the optimal Holder exponent of the integrated density of states, the dimension of the density of states measure, the dimension of the spectrum, and the upper transport exponent) and the dynamical properties of the Fibonacci trace map (such as dimensional characteristics of the non-wand...
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作者：Kwapisz, Jaroslaw
作者单位：Montana State University System; Montana State University Bozeman
摘要：We prove that any expanding linear map that is the inflation map in an inflation-substitution process generating a self-affine tiling of is integral algebraic and Perron. This means that is linearly conjugate to a restriction of an integer matrix to a subspace satisfying a maximal growth condition that generalizes the characterization of Perron numbers as numbers that are larger than the moduli of their algebraic conjugates. The case of diagonalizable has been previously resolved by Richard Ke...
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作者：Fayad, Bassam; Kanigowski, Adam
作者单位：Sorbonne Universite; Universite Paris Cite; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：Arnold and Kochergin mixing conservative flows on surfaces stand as the main and almost only natural class of mixing transformations for which higher order mixing has not been established, nor disproved. Under suitable arithmetic conditions on their unique rotation vector, of full Lebesgue measure in the first case and of full Hausdorff dimension in the second, we show that these flows are mixing of any order. For this, we show that they display a generalization of the so called Ratner propert...
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作者：Liu, Jinsong; Zhou, Ze
作者单位：Chinese Academy of Sciences; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：The midscribability theorem, which was first proved by O. Schramm, states that: given a smooth strictly convex body and a convex polyhedron , there exists a convex polyhedron combinatorially equivalent to which midscribes . Here the word midscribe means that all its edges are tangent to the boundary surface of . By using the intersection number technique, together with the Teichmuller theory of packings, this paper provides an alternative approach to this theorem. Furthermore, by combining Sch...
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作者：McLean, Mark
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：Let A be an affine variety inside a complex N dimensional vector space which has an isolated singularity at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact manifold contactomorphic to the link of A is said to be Milnor fillable by A. If the first Chern class of our link is torsion then we can assign an invariant of our singularity called the minimal discrepancy, which is an important invariant in birational geometr...
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作者：Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael
作者单位：Universite Bourgogne Europe; Centre National de la Recherche Scientifique (CNRS); State University of New York (SUNY) System; Binghamton University, SUNY; Universidad de la Republica, Uruguay
摘要：We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms f on compact 3-manifolds with fundamental groups of exponential growth such that is not homotopic to identity for all . These provide counterexamples to a classification conjecture of Pujals.
