We examine the existence of rational divisors on modular curves of 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.
|Original language||English (US)|
|Number of pages||15|
|Journal||Journal of Number Theory|
|State||Published - Mar 2013|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory