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• Unramified division algebras do not always contain Azumaya maximal orders AI翻译
  作者：Antieau, Benjamin; Williams, Ben
  作者单位：University of California System; University of California Los Angeles; University of Southern California
  摘要：We show that, in general, over a regular integral noetherian affine scheme X of dimension at least 6, there exist Brauer classes on X for which the associated division algebras over the generic point have no Azumaya maximal orders over X. Despite the algebraic nature of the result, our proof relies on the topology of classifying spaces of algebraic groups.
• On the Cauchy problem for gravity water waves AI翻译
  作者：Alazard, T.; Burq, N.; Zuily, C.
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
  摘要：We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider turn out to be only of -class for some and consequently have unbounded curvature, while the initial velocities are only Lipschitz. We reduce the system using a paradifferential approach.
• Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space (vol 180, pg 559, 2010) AI翻译
  作者：Bauer, I.; Catanese, F.
  作者单位：University of Bayreuth
• Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions AI翻译
  作者：Jia, Hao; Sverak, Vladimir
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.
• On special zeros of p-adic L-functions of Hilbert modular forms AI翻译
  作者：Spiess, Michael
  作者单位：University of Bielefeld
  摘要：Let E be a modular elliptic curve over a totally real number field F. We prove the weak exceptional zero conjecture which links a (higher) derivative of the p-adic L-function attached to E to certain p-adic periods attached to the corresponding Hilbert modular form at the places above p where E has split multiplicative reduction. Under some mild restrictions on p and the conductor of E we deduce the exceptional zero conjecture in the strong form (i.e. where the automorphic p-adic periods are r...
• The Iwasawa Main Conjectures for GL2 AI翻译
  作者：Skinner, Christopher; Urban, Eric
  作者单位：Princeton University; Sorbonne Universite; Universite Paris Cite; Columbia University
  摘要：We prove the one-, two-, and three-variable Iwasawa-Greenberg Main Conjectures for a large class of modular forms that are ordinary with respect to an odd prime p. The method of proof involves an analysis of an Eisenstein ideal for ordinary Hida families for GU(2,2).
• Joint quasimodes, positive entropy, and quantum unique ergodicity AI翻译
  作者：Brooks, Shimon; Lindenstrauss, Elon
  作者单位：Bar Ilan University; Hebrew University of Jerusalem
  摘要：We study joint quasimodes of the Laplacian and one Hecke operator on compact congruence surfaces, and give conditions on the orders of the quasimodes that guarantee positive entropy on almost every ergodic component of the corresponding semiclassical measures. Together with the measure classification result of (Lindenstrauss, Ann Math (2) 163(1):165-219, 2006), this implies Quantum Unique Ergodicity for such functions. Our result is optimal with respect to the dimension of the space from which...
• Monodromy of cyclic coverings of the projective line AI翻译
  作者：Venkataramana, T. N.
  作者单位：Tata Institute of Fundamental Research (TIFR)
  摘要：We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of ramification points is sufficiently large compared to the degree d and the ramification degrees are co-prime to d.
• A fully anisotropic mechanism for formation of trapped surfaces in vacuum AI翻译
  作者：Klainerman, Sergiu; Luk, Jonathan; Rodnianski, Igor
  作者单位：Princeton University; University of Pennsylvania; Massachusetts Institute of Technology (MIT)
  摘要：We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide local conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat in all other directions) whose future development contains a trapped surface. This extends considerably the previous result of Christodoulou (Monographs in Mathematics. European Mathematical Society, Switzerland, 2009) which required instead a uniform condition along al...
• Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations AI翻译
  作者：Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
  作者单位：University of Kansas; Universite Claude Bernard Lyon 1; Indiana University System; Indiana University Bloomington
  摘要：We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time behavior is governed by an associated second-order formal Whitham modulation system. A key point is to identify the way in which initial perturbations translate to initial data for this formal system, a task accomplished by detailed estimates on the linearized ...