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

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

2011-03-30

arxiv.org/abs/1103.5833v1

Mathematics

Number Theory

13 pages

Scientific paper

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.

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