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作者：Guralnick, Robert M.; Liebeck, Martin W.; O'Brien, E. A.; Shalev, Aner; Tiep, Pham Huu
作者单位：University of Southern California; Imperial College London; University of Auckland; Hebrew University of Jerusalem; Rutgers University System; Rutgers University New Brunswick
摘要：We prove surjectivity of certain word maps on finite non-abelian simple groups. More precisely, we prove the following: if N is a product of two prime powers, then the word map is surjective on every finite non-abelian simple group; if N is an odd integer, then the word map is surjective on every finite quasisimple group. These generalize classical theorems of Burnside and Feit-Thompson. We also prove asymptotic results about the surjectivity of the word map that depend on the number of prime ...
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作者：Ilyashenko, Yu.; Kudryashov, Yu.; Schurov, I.
作者单位：HSE University (National Research University Higher School of Economics); Cornell University
摘要：We construct an open set of structurally unstable three parameter families whose weak and so called moderate topological classification defined below has a numerical invariant that may take an arbitrary positive value. Here and below families are families of vector fields in the two-sphere. This result disproves an Arnold's conjecture of 1985. Then we construct an open set of six parameter families whose moderate topological classification has a functional invariant. This invariant is an arbit...
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作者：Mayboroda, Svitlana; Maz'ya, Vladimir
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Linkoping University; Peoples Friendship University of Russia
摘要：In the present paper we establish the Wiener test for boundary regularity of the solutions to the polyharmonic operator. We introduce a new notion of polyharmonic capacity and demonstrate necessary and sufficient conditions on the capacity of the domain responsible for the regularity of a polyharmonic function near a boundary point. In the case of the Laplacian the test for regularity of a boundary point is the celebrated Wiener criterion of 1924. It was extended to the biharmonic case in dime...
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作者：Kleinbock, D. Y.; Margulis, G. A.
作者单位：Brandeis University; Yale University
摘要：One of the propositions in the paper (Kleinbock and Margulis in Invent Math 138(3):451-494, 1999), related to approximating certain sets by smooth functions, was recently found to be incorrect. Here, we correct the mistake.
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作者：Boehm, Christoph; Lafuente, Ramiro A.
作者单位：University of Munster
摘要：We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.
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作者：Ma, Linquan; Schwede, Karl
作者单位：Purdue University System; Purdue University; Utah System of Higher Education; University of Utah
摘要：Using perfectoid algebras we introduce a mixed characteristic analog of the multiplier ideal, respectively test ideal, from characteristic zero, respectively in the case of a regular ambient ring. We prove several properties about this ideal such as subadditivity. We then use these techniques to derive a uniform bound on the growth of symbolic powers of radical ideals in all excellent regular rings. The analogous result was shown in equal characteristic by Ein-Lazarsfeld-Smith and Hochster-Hun...
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作者：Bhatt, Bhargav
作者单位：University of Michigan System; University of Michigan
摘要：Andre recently gave a beautiful proof of Hochster's direct summand conjecture in commutative algebra using perfectoid spaces; his two main results are a generalization of the almost purity theorem (the perfectoid Abhyankar lemma) and a construction of certain faithfully flat extensions of perfectoid algebras where discriminants acquire all p-power roots. In this paper, we explain a quicker proof of Hochster's conjecture that circumvents the perfectoid Abhyankar lemma; instead, we prove and use...
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作者：Viet-Anh Nguyen
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille
摘要：We study the holonomy cocycle H of a holomorphic foliation F by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions: its singularities E are all hyperbolic; there is no holomorphic non-constant map C -> X such that out of E the image of C is locally contained in a leaf. Let T be a harmonic current tangent to F which does not give mass to any invariant analytic curve. Using the leafwise Poincare metric, we show that H is integrable with res...
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作者：Bourque, Maxime Fortier
作者单位：University of Toronto
摘要：We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy class is homotopy equivalent to a point, a circle, a torus, or the unit tangent bundle of the codomain, depending on the induced homomorphism on fundamental groups. Quadratic differentials play a central role in the proof.
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作者：Dudas, Olivier; Malle, Gunter
作者单位：Universite Paris Cite; University of Kaiserslautern
摘要：We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after -reduction. To this end, we construct a progenerator for the category of representations of a finite reductive group coming from generalised Gelfand-Graev representations. This is achieved by showing that cuspidal representations appear in the head of generalised Gelfand-Graev representations attached to cuspidal unipotent classes, as defined and studied in Geck and Malle (J L...
