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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...
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作者：[Anonymous]
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作者：Popa, Mihnea; Schnell, Christian
作者单位：Northwestern University; State University of New York (SUNY) System; Stony Brook University
摘要：We use the theory of Hodge modules to construct Viehweg-Zuo sheaves on base spaces of families with maximal variation and fibers of general type and, more generally, families whose geometric generic fiber has a good minimal model. Combining this with a result of Campana-Pun, we deduce Viehweg's hyperbolicity conjecture in this context, namely the fact that the base spaces of such families are of log general type. This is approached as part of a general problem of identifying what spaces can su...
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作者：Pilloni, Vincent
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Nous montrons un th,orSme de rel,vement modulaire pour des repr,sentations galoisiennes p-adiques de dimension 2, non-ramifi,es en p, des corps totalement r,els peu ramifi,s en p.
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作者：Damanik, David; Goldstein, Michael; Lukic, Milivoje
作者单位：Rice University; University of Toronto
摘要：We study the quasi-periodic Schrodinger operator -psi ''(x) + V(x)psi(x) = E psi(x), x is an element of R in the regime of small V(x) = Sigma(m is an element of Zv) c(m) exp(2 pi im omega x), omega = (omega(1), ... , omega(v)) is an element of R-v, vertical bar c(m)vertical bar <= epsilon exp(-kappa(0)vertical bar m vertical bar). We show that the set of reflectionless potentials isospectral with V is homeomorphic to a torus. Moreover, we prove that any reflectionless potential Q isospectral w...
