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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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On Néron class groups of abelian varieties

1Departamento de Matemáticas, Universidad de La Serena, Chile

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2012, Issue 664, Pages 71–91, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2011.109, June 2011

Publication History

Received:
2009-09-29
Revised:
2010-09-29
Published Online:
2011-06-28

Abstract

Let F be a global field, let S be the set of archimedean primes of F and let S be any nonempty finite set of primes of F containing S. In this paper we study the Néron S-class group CA, F, S of an abelian variety A defined over F. In the well-known analogy that exists between the Birch and Swinnerton–Dyer conjecture for A over F and the analytic class number formula for the field F (in the number field case), the finite group CA, F, S (not the Tate–Shafarevich group of A) is a natural analog of the ideal class group of F.

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