D-elliptic sheaves and odd Jacobians

Research output: Contribution to journalArticle

Abstract

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 languageEnglish (US)
Pages (from-to)1012-1026
Number of pages15
JournalJournal of Number Theory
Volume133
Issue number3
DOIs
StatePublished - Mar 1 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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