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Manuscripta Mathematica

, Volume 134, Issue 3–4, pp 475–484 | Cite as

A Stickelberger index for the Tate-Shafarevich group revisited

  • Petra ForsterEmail author
  • Hendrik Kasten
Article
  • 48 Downloads

Abstract

We obtain an algebraic description of the critical value of the L-series of an elliptic curve of rank zero over an abelian number field with conductor coprime to the one of the curve. We do this by construction of matching Stickelberger-ideals and computation of their indices. By inserting the result into the formula of the conjecture of Birch and Swinnerton-Dyer we can describe the order of the Tate-Shafarevich group by a number of algebraic expressions.

Mathematics Subject Classification (2000)

11G05 11F11 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institut für Algebra und GeometrieUniversität KarlsruheKarlsruheGermany
  2. 2.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany

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