Regulator constants and the parity conjecture

• 成果类型: Article
• 署名作者: Dokchitser, Tim; Dokchitser, Vladimir
• 署名单位: University of Cambridge; University of Cambridge
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0193-7
• 发表日期: 2009
• 页码: 23-71
• 关键词: elliptic-curves; abelian-varieties; selmer groups; root numbers; FIELDS; GROWTH; birch; rank

摘要

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p(infinity)-Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K-infinity is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K-infinity/Q). We also give analogous results when K/Q is non-abelian, the base field is not Q and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of finite groups, their regulator constants, and compatibility between local root numbers and local Tamagawa numbers of abelian varieties in such relations.