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Hypergeometric Abelian Varieties

Published online by Cambridge University Press:  20 November 2018

Natália Archinard
Natália Archinard*
Affiliation:
McGill University, Montreal, Quebec e-mail: [email protected]
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Abstract

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In this paper, we construct abelian varieties associated to Gauss’ and Appell–Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, Wüstholz), modular embeddings (Cohen, Wolfart) to CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon). Our contribution is to provide a complete, explicit and self-contained geometric construction.

Keywords

1114
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 5 , 01 October 2003 , pp. 897 - 932
Copyright
Copyright © Canadian Mathematical Society 2003

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