Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 10 (2013), 2511-2544.
On the second Tate–Shafarevich group of a 1-motive
We prove finiteness results for Tate–Shafarevich groups in degree associated with -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 . We also establish an arithmetic duality theorem for -motives over number fields, which complements earlier results of Harari and Szamuely.
Algebra Number Theory, Volume 7, Number 10 (2013), 2511-2544.
Received: 27 September 2012
Revised: 4 March 2013
Accepted: 11 April 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]
Secondary: 14G25: Global ground fields 14G20: Local ground fields
Jossen, Peter. On the second Tate–Shafarevich group of a 1-motive. Algebra Number Theory 7 (2013), no. 10, 2511--2544. doi:10.2140/ant.2013.7.2511. https://projecteuclid.org/euclid.ant/1513730115