Endomorphism algebras of factors of certain hypergeometric Jacobians

Abstract

We classify the endomorphism algebras of factors of the Jacobians 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 = Q ( ζ q ) E=\mathbb {Q}(\zeta _q) , or a quadratic extension of E E , or E ⊕ E 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 C \mathbb {C} .