Regulator constants and the parity conjecture

TY Dokchitser, V Dokchitser

Research output: Contribution to journalArticle (Academic Journal)peer-review

37 Citations (Scopus)

Abstract

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p ∞-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 ∞ is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of . 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.
Translated title of the contributionRegulator constants and the parity conjecture
Original languageEnglish
Pages (from-to)23 - 71
Number of pages49
JournalInventiones Mathematicae
Volume178
Issue number1
DOIs
Publication statusPublished - Oct 2009

Bibliographical note

Publisher: Springer

Fingerprint Dive into the research topics of 'Regulator constants and the parity conjecture'. Together they form a unique fingerprint.

Cite this