CAPPING GROUPS AND SOME CASES OF THE FONTAINE-MAZUR CONJECTURE

Frauke M Bleher; Ted Chinburg; Jennifer Froelich

doi:10.1090/S0002-9939-08-09677-9

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CAPPING GROUPS AND SOME CASES OF THE FONTAINE-MAZUR CONJECTURE

Journal article

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CAPPING GROUPS AND SOME CASES OF THE FONTAINE-MAZUR CONJECTURE

Frauke M Bleher, Ted Chinburg and Jennifer Froelich

Proceedings of the American Mathematical Society, Vol.137(5), pp.1551-1560

01/01/2009

DOI: 10.1090/S0002-9939-08-09677-9

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Abstract

In this paper we will prove some cases of the Fontaine-Mazur conjecture. Let p be an odd prime and let G(Q,{p}) be the Galois group over Q of the maximal unramified-outside-p extension of Q. We show that tinder certain hypotheses, the universal deformation of the action of G(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 (S) over cap (4) caps Q for the prime 2, where (S) over cap (4) is the double cover of S(4) whose Sylow 2-subgroups are generalized quaternion groups.

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Physical Sciences

Mathematics, Applied

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Details

Title: Subtitle: CAPPING GROUPS AND SOME CASES OF THE FONTAINE-MAZUR CONJECTURE
Creators: Frauke M Bleher - University of Iowa
Ted Chinburg - University of Pennsylvania
Jennifer Froelich - Dickinson College
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.137(5), pp.1551-1560
DOI: 10.1090/S0002-9939-08-09677-9
ISSN: 0002-9939
eISSN: 1088-6826
Publisher: American Mathematical Society
Number of pages: 10
Grant note: DMS06-51332; DMS05-00106 / NSF H98230-06-1-0021 / NSA
Language: English
Date published: 01/01/2009
Academic Unit: Mathematics
Record Identifier: 9984240867602771

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