Vol. 7, No. 10, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
On the second Tate–Shafarevich group of a 1-motive

Peter Jossen

Vol. 7 (2013), No. 10, 2511–2544
Abstract

We prove finiteness results for Tate–Shafarevich groups in degree 2 associated with 1-motives. We give a number-theoretic interpretation of these groups, relate them to Leopoldt’s conjecture, and present an example of a semiabelian variety with an infinite Tate–Shafarevich group in degree 2. We also establish an arithmetic duality theorem for 1-motives over number fields, which complements earlier results of Harari and Szamuely.

Keywords
$1$-motives, semiabelian varieties, Tate–Shafarevich groups
Mathematical Subject Classification 2010
Primary: 14K15
Secondary: 14G25, 14G20
Milestones
Received: 27 September 2012
Revised: 4 March 2013
Accepted: 11 April 2013
Published: 18 January 2014
Authors
Peter Jossen
CNRS, UMR 8628
Mathématiques
Université Paris-Sud
Bâtiment 425
91450 Orsay
France