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A Stickelberger-Index for the Tate-Shafarevich Group
by
Hendrik Kasten
Mathematisches Institut II, Universit"at Karlsruhe, Germany
In this paper, we obtain an algebraic description of the critical value of the L-series of a class of elliptic curves over an arbitrary real abelian number field. We do this by construction of a matching Stickelberger-ideal and computation of its index. 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.
Date received: April 23, 2004
Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # calz-58.