2011/03/30 by Mihran Papikian, Papikian, Mihran
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.NT
paper · pdf · doi:10.48550/arxiv.1103.5833
13 pages
arxiv created 2011/03/30 · arxiv updated 2011/03/31
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.