# Generalized Legendre Curves And Quaternionic Multiplication

Alyson Deines, Jenny G. Fuselier, Ling Long, Holly Swisher, Fang-Ting Tu

Published 2016 · Mathematics

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.

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