English

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

Number Theory 2011-03-31 v1

Abstract

We examine the existence of rational divisors on modular curves of D\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.

Keywords

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

R2 v1 2026-06-21T17:46:46.948Z