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On the number of cusps of orthogonal Shimura varieties

Content Provider	Springer Nature Link
Author	Attwell Duval, Dylan
Copyright Year	2014
Abstract	We study the cusps of Shimura varieties arising from indefinite lattices splitting two hyperbolic planes. We determine the number of 0-dimensional cusps for a given variety and, when the lattice is maximal, we relate the genus of the lattice to the number of $$1$$ -dimensional cusps and determine an explicit formula. As every lattice is contained as a sublattice of finite index in a maximal lattice, the results we obtain are useful in a general analysis.Nous étudions les pointes des variétés de Shimura apparaissant dans les treillis indéfinis séparant deux plans hyperboliques. Nous déterminons le nombre de pointes de dimension 0 pour une variété donnée et, lorsque le treillis est maximal, nous relions le genre du treillis et le nombre de pointes de dimension 1 via une formule explicite. Comme tout treillis est contenu, en tant que sous-treillis, dans un treillis maximal, les résultats obtenus sont utiles en général.
Starting Page	119
Ending Page	131
Page Count	13
File Format	PDF
ISSN	21954755
Journal	Annales mathématiques du Québec
Volume Number	38
Issue Number	2
e-ISSN	21954763
Language	English
Publisher	Springer International Publishing
Publisher Date	2014-11-22
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Modular and Shimura varieties Cusps Algebra Quadratic forms Analysis Hyperbolic planes Mathematics Quadratic forms over global rings and fields Number Theory Shimura varieties Isotropic planes
Content Type	Text
Resource Type	Article
Subject	Mathematics

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