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Abelian varieties with quaternion and complex multiplication

2012/08/28 by Dominik Ufer, Ufer, Dominik
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1208.5599

Abstract

In this paper we study abelian varieties which correspond to CM points in the coarse moduli space of principally polarized abelian varieties with multiplication by a maximal order in a quaternion algebra over a totally real number field. These are abelian varieties of even dimension with quaternion and complex multiplication. We describe them explicitly via isogenies to products of abelian varieties of smaller dimension together with estimates on the degree of the isogeny.

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