$\mathcal{D}$-elliptic sheaves and odd Jacobians
Number Theory
2011-03-31 v1
Abstract
We examine the existence of rational divisors on modular curves of -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.
Cite
@article{arxiv.1103.5833,
title = {$\mathcal{D}$-elliptic sheaves and odd Jacobians},
author = {Mihran Papikian},
journal= {arXiv preprint arXiv:1103.5833},
year = {2011}
}
Comments
13 pages