Inventiones mathematicae

, 178:23

Regulator constants and the parity conjecture


    • Robinson College
  • Vladimir Dokchitser
    • Gonville & Caius College

DOI: 10.1007/s00222-009-0193-7

Cite this article as:
Dokchitser, T. & Dokchitser, V. Invent. math. (2009) 178: 23. doi:10.1007/s00222-009-0193-7


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 \(\mathop{\mathrm{Gal}}(K^{\infty}/{\mathbb{Q}})\) . 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.

Mathematics Subject Classification (2000)


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© Springer-Verlag 2009