Title

Capping Groups and Some Cases of the Fontaine-Mazur Conjecture

Document Type

Article

Publication Date

5-2009

Department

Mathematics

Language

English

Publication Title

Proceedings of the American Mathematical Society

Abstract

In this paper we will prove some cases of the Fontaine-Mazur conjecture. Let p be an odd prime and let $G_{{\Bbb Q},\{p\}}$ be the Galois group over ℚ of the maximal unramified-outside-p extension of ℚ. We show that under certain hypotheses, the universal deformation of the action of $G_{{\Bbb Q},\{p\}}$ on the 2-torsion of an elliptic curve defined over ℚ has finite image. We compute the associated universal deformation ring, and we show in the process that Ŝ₄ caps ℚ for the prime 2, where Ŝ₄ is the double cover of S₄ whose Sylow 2-subgroups are generalized quaternion groups.

Comments

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