D-elliptic sheaves and odd Jacobians

Mihran Papikian

doi:10.1016/j.jnt.2012.02.005

D-elliptic sheaves and odd Jacobians

Mihran Papikian

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1012-1026
Number of pages	15
Journal	Journal of Number Theory
Volume	133
Issue number	3
DOIs	https://doi.org/10.1016/j.jnt.2012.02.005
State	Published - Mar 2013

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2012.02.005

Cite this

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title = "D-elliptic sheaves and odd Jacobians",

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.",

author = "Mihran Papikian",

note = "Funding Information: 1 The author was supported in part by NSF grant DMS-0801208.",

year = "2013",

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N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84892526232#tab=citedBy

U2 - 10.1016/j.jnt.2012.02.005

DO - 10.1016/j.jnt.2012.02.005

M3 - Article

AN - SCOPUS:84892526232

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SP - 1012

EP - 1026

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 3

ER -

D-elliptic sheaves and odd Jacobians

Abstract

All Science Journal Classification (ASJC) codes

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