Special values of L-functions and false Tate curve extensions

Bouganis, A.

Abstract

In this paper we show how the p-adic Rankin–Selberg product construction of Hida can be combined with freeness results of Hecke modules of Wiles to establish interesting congruences between particular special values of L-functions of elliptic curves. These congruences are part of some deep conjectural congruences that follow from the work of Kato on the non-commutative Iwasawa theory of the false Tate curve extension. In the appendix by Vladimir Dokchitser it is shown that these congruences, combined with results from Iwasawa theory for elliptic curves, give interesting results for the arithmetic of elliptic curves over non-abelian extensions.

Citation

Bouganis, A. (2010). Special values of L-functions and false Tate curve extensions. Journal of the London Mathematical Society, 82(3), 596-620. https://doi.org/10.1112/jlms/jdq041

• Journal Article Type: Article
• Acceptance Date: Jan 21, 2010
• Online Publication Date: Sep 20, 2010
• Publication Date: Sep 20, 2010
• Deposit Date: Sep 18, 2013
• Publicly Available Date: Apr 11, 2017
• Journal: Journal of the London Mathematical Society
• Print ISSN: 0024-6107
• Electronic ISSN: 1469-7750
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 82
• Issue: 3
• Pages: 596-620
• DOI: https://doi.org/10.1112/jlms/jdq041
• Public URL: https://durham-repository.worktribe.com/output/1449860