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作者：Liu, Ruochuan; Zhu, Xinwen
作者单位：Peking University; California Institute of Technology
摘要：We construct a functor from the category of p-adic ,tale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection on its base change to , which can be regarded as a first step towards the sought-after p-adic Riemann-Hilbert correspondence. As a consequence, we obtain the following rigidity theorem for p-adic local systems on a connected rigid analytic variety: if the stalk of such a local system at one point, regarde...
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作者：Botvinnik, Boris; Ebert, Johannes; Randal-Williams, Oscar
作者单位：University of Oregon; University of Munster; University of Cambridge
摘要：We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary index map from the space of positive scalar metrics to a suitable space from the real K-theory spectrum. Our main results concern the nontriviality of this map. We prove that for 2n >= 6, the natural KO-orientation from the infinite loop space of ...
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作者：He, Hongyu
作者单位：Louisiana State University System; Louisiana State University
摘要：In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the discrete series of U(p, q). There are three themes in this paper: branching laws of a small A(q) (lambda) branching laws of discrete series and inductive construction of discrete series. These themes are linked together by a reciprocity law and the notion of invariant tensor product.
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作者：Casals, Roger; Luis Perez, Jose; del Pino, Alvaro; Presas, Francisco
作者单位：Massachusetts Institute of Technology (MIT); Autonomous University of Madrid; Universidad Carlos III de Madrid; Complutense University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM)
摘要：In this article we prove that the inclusion of the space of Engel structures of a smooth 4-manifold into the space of full flags of its tangent bundle induces surjections in all homotopy groups. In particular, we construct Engel structures representing any given full flag.
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作者：Avila, A.; Jitomirskaya, S.; Marx, C. A.
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of California System; University of California Irvine; University System of Ohio; Oberlin College
摘要：The extended Harper's model, proposed by D.J. Thouless in 1983, generalizes the famous almost Mathieu operator, allowing for a wider range of lattice geometries (parametrized by three coupling parameters) by permitting 2D electrons to hop to both nearest and next nearest neighboring (NNN) lattice sites, while still exhibiting its characteristic symmetry (Aubry-Andre duality). Previous understanding of the spectral theory of this model was restricted to two dual regions of the parameter space, ...
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作者：Wilms, Robert
作者单位：Johannes Gutenberg University of Mainz
摘要：In this paper we give new explicit formulas for Faltings' -invariant in terms of integrals of theta functions, and we deduce an explicit lower bound for only in terms of the genus and an explicit upper bound for the Arakelov-Green function in terms of . Furthermore, we give a canonical extension of and the Zhang-Kawazumi invariant to the moduli space of indecomposable principally polarised complex abelian varieties.
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作者：Armstrong, Scott; Kuusi, Tuomo; Mourrat, Jean-Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; New York University; Aalto University; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：One of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In this paper, we address this problem in a new way, in the context of linear elliptic equations in divergence form, by showing that certain quantities associated to the energy density of solutions are essentially additive. As a result, we are able to prove quantitative estimates on the wea...
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作者：Heath-Brown, D. R.; Li, Xiannan
作者单位：University of Oxford
摘要：We prove an asymptotic formula for the number of primes of the shape , thereby refining the well known work of Friedlander and Iwaniec (Ann Math (2) 148(3):945-1040, 1998). Along the way, we prove a result on equidistribution of primes up to x, in which the moduli may be almost as large as x(2).
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作者：Minguez, Alberto; Secherre, Vincent
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Let be a non-Archimedean local field of residual characteristic p, and be a prime number different from p. We consider the local Jacquet-Langlands correspondence between -adic discrete series of and an inner form . We show that it respects the relationship of congruence modulo . More precisely, we show that two integral -adic discrete series of are congruent modulo if and only if the same holds for their Jacquet-Langlands transfers to . We also prove that the Langlands-Jacquet morphism from th...
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作者：Colmez, Pierre; Niziol, Wieslawa
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：We compute syntomic cohomology of semistable affinoids in terms of cohomology of (phi, Gamma)-modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known to compute Galois cohomology of these affinoids. For a semistable scheme over a mixed characteristic local ring this implies a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves. This generalizes the comparison results of Kat...
