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Hypergeometric Abelian Varieties

  Published:2003-10-01
 Printed: Oct 2003
  • Natália Archinard
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Abstract

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, W\"ustholz), 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.
MSC Classifications: 11, 14 show english descriptions unknown classification 11
unknown classification 14
11 - unknown classification 11
14 - unknown classification 14
 

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