Abelian L-Functions at s=1 and Explicit Reciprocity for Rubin-Stark Elements

dc.creatorSolomon, David
dc.date2007-02-13
dc.date2008-07-10
dc.date.accessioned2026-07-07T09:49:27Z
dc.date.available2026-07-07T09:49:27Z
dc.descriptionGiven an abelian, CM extension K of any totally real number field k, we consider two conjectures `of Stark type'. The `Integrality Conjecture' concerns the image of a p-adic map `\mathfrak{s}_{K/k,S}' determined by the minus-part of the S-truncated equivariant L-function for K/k at s=1. It is connected to the Equivariant Tamagawa Number Conjecture of Burns and Flach. The `Congruence Conjecture' says that \mathfrak{s}_{K/k,S} gives an explicit reciprocity law for the element predicted by the corresponding Rubin-Stark Conjecture for K^+/k. We study the general properties of these conjectures and prove one or both of them under various hypotheses, notably when p does not divide [K:k], when k=Q or when K is absolutely abelian.
dc.description41 pages. Several misprints corrected. Other minor changes
dc.identifierhttps://arxiv.org/abs/math/0702387
dc.identifierhttp://arxiv.org/abs/math/0702387
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164595
dc.subjectNumber Theory
dc.subject11R42; 11S31
dc.titleAbelian L-Functions at s=1 and Explicit Reciprocity for Rubin-Stark Elements
dc.typetext

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