On a question of Ekedahl and Serre

Ke Chen, Xin Lu, Kang Zuo

Published 2017-03-30Version 1

In this paper we study the Ekedahl-Serre conjecture over number fields. The main result is the existence of an upper bound for the genus of curves whose Jacobians admit isogenies of bounded degrees to self-products of a given elliptic curve over a number field satisfying the Sato-Tate equidistribution, and the technique is motivated by similar results over function field due to Kukulies. A few variants are considered and questions involving more general Shimura subvarieties are discussed.