Regulator constants and the parity conjecture

By Tim Dokchitser, Vladimir Dokchitser. 2007

83 citations recorded by the source corpus.

AbstractThe 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c2a20c80da94795a0f920ba4eabfc1984b7a5781

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In Geometry and Topology

1. Tim Dokchitser
2. Vladimir Dokchitser
3. Manjul Bhargava
4. A. Shankar

In Mathematical Physics

1. Vladimir Dokchitser
2. Tim Dokchitser
3. Manjul Bhargava
4. A. Shankar

Citations in the corpus

• Root numbers, Selmer groups, and non-commutative Iwasawa theory (2010, unknown): “Root numbers, Selmer groups, and non-commutative Iwasawa theory John Coates, Takako Fukaya, Kazuya Kato, Ramdorai Sujatha November 4, 2008”
• On the Birch-Swinnerton-Dyer quotients modulo squares (2006, background): “We now turn to Tamagawa numbers and their relation to root numbers, in the special case of elliptic curves.”