Endomorphism algebras of factors of certain hypergeometric Jacobians

Abstract

We classify the endomorphism algebras of factors of the Jacobian of certain hypergeometric curves over a field of characteristic zero. Other than a few exceptional cases, the endomorphism algebras turn out to be either a cyclotomic field $E=\mathbb{Q}(\zeta_q)$, or a quadratic extension of $E$, or $E\oplus E$. This result may be viewed as a generalization of the well known results of the classification of endomorphism algebras of elliptic curves over $\mathbb{C}$.