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Topological and algebraic results on the boundary of connected orthogonal Shimura varieties

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Abstract

We study the boundary of orthogonal Shimura varieties associated to a positive multiple of a maximal lattice splitting two hyperbolic planes. We provide closed formulas for the number of 0 and 1-dimensional cusps of these spaces and study their configuration within the boundary. This generalizes our earlier results about maximal lattices.

Résumé

Nous étudions la frontière des variétés orthogonales de Shimura associées à un multiple positif d’un treillis maximal scindant deux plans hyperboliques. Nous obtenons des formules closes pour le nombre de pointes de dimension 0 et de dimension 1 pour ces espaces et nous étudions leur configuration à l’intérieur de la frontière. Ceci généralise nos résultats précédents concernant les treillis maximaux.

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Acknowledgments

The ideas for this paper came out of the author’s Ph.D. studies, part of which were funded by a grant from the Natural Sciences and Engineering Research Council of Canada. The author would like to thank his Ph.D. supervisor, Prof. Eyal Goren, for his suggestions and assistance in editing.

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Correspondence to Dylan Attwell-Duval.

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Attwell-Duval, D. Topological and algebraic results on the boundary of connected orthogonal Shimura varieties. Ann. Math. Québec 41, 27–42 (2017). https://doi.org/10.1007/s40316-016-0067-5

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  • DOI: https://doi.org/10.1007/s40316-016-0067-5

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