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
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.