Abelian L-Functions at s=1 and Explicit Reciprocity for Rubin-Stark Elements
| dc.creator | Solomon, David | |
| dc.date | 2007-02-13 | |
| dc.date | 2008-07-10 | |
| dc.date.accessioned | 2026-07-07T09:49:27Z | |
| dc.date.available | 2026-07-07T09:49:27Z | |
| dc.description | Given 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.description | 41 pages. Several misprints corrected. Other minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0702387 | |
| dc.identifier | http://arxiv.org/abs/math/0702387 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164595 | |
| dc.subject | Number Theory | |
| dc.subject | 11R42; 11S31 | |
| dc.title | Abelian L-Functions at s=1 and Explicit Reciprocity for Rubin-Stark Elements | |
| dc.type | text |