Shimura curves embedded in Igusa's threefold
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus Q_O of quaternionic multiplication by O in the moduli space A_g of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe Q_O as a union of Atkin-Lehner quotients of Shimura varieties and we compute the number of irreducible components of Q_O in terms of class numbers of CM-fields.
Cite
@article{arxiv.math/0312435,
title = {Shimura curves embedded in Igusa's threefold},
author = {Victor Rotger},
journal= {arXiv preprint arXiv:math/0312435},
year = {2007}
}
Comments
To appear in Modular curves and Abelian varieties, Progress in Mathematics 224 Birkhauser, (2003), 263-273