Generalized Legendre curves and Quaternionic Multiplication
Number Theory
2015-11-23 v3
Abstract
This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of 2-dimensional abelian varieties of this kind, we determine when the endomorphism algebra of each fiber defined over the algebraic closure of contains a quaternion algebra.
Cite
@article{arxiv.1412.6906,
title = {Generalized Legendre curves and Quaternionic Multiplication},
author = {Alyson Deines and Jenny G. Fuselier and Ling Long and Holly Swisher and Fang-Ting Tu},
journal= {arXiv preprint arXiv:1412.6906},
year = {2015}
}