Title

Generalized Legendre curves and quaternionic multiplication

Document Type

Article

Publication Date

1-1-2016

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 Q contains a quaternion algebra.

Publication Source (Journal or Book title)

Journal of Number Theory

First Page

175

Last Page

203

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