$\mathcal{D}$-elliptic sheaves and odd Jacobians

Abstract

We examine the existence of rational divisors on modular curves of $\mathcal{D}$-elliptic sheaves and on Atkin-Lehner quotients of these curves over local fields. Using a criterion of Poonen and Stoll, we show that in infinitely many cases the Tate-Shafarevich groups of the Jacobians of these Atkin-Lehner quotients have non-square orders.

13 pages

References in corpus (1)

• Twists of Drinfeld-Stuhler modular varieties