Discrete groups, Mumford curves and Theta functions
نویسندگان
چکیده
منابع مشابه
Theta functions on covers of symplectic groups
We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$. This representation is obtained from the residues of Eisenstein series on this group. If $r$ is odd, $nle r
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We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.
متن کاملAlgorithms for Mumford curves
Mumford showed that Schottky subgroups of PGL(2,K) give rise to certain curves, now called Mumford curves, over a non-archimedean field K. Such curves are foundational to subjects dealing with nonarchimedean varieties, including Berkovich theory and tropical geometry. We develop and implement numerical algorithms for Mumford curves over the field of p-adic numbers. A crucial and difficult step ...
متن کاملMumford-tate Groups
Much of the use of Mumford-Tate groups has been in the classical case of weight one polarized Hodge structures (theory of Shimura varieties). Since this topic will be covered elsewhere in the summer school, this set of lectures will emphasize the non-classical, higher weight case which is much less explored. The first four of these lectures will be largely self-contained, making use of the lect...
متن کاملSpectral triples from Mumford curves
We construct spectral triples associated to Schottky–Mumford curves, in such a way that the local Euler factor can be recovered from the zeta functions of such spectral triples. We propose a way of extending this construction to the case where the curve is not k-split degenerate.
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 1992
ISSN: 0240-2963
DOI: 10.5802/afst.754