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Computation of a universal deformation ring in the Borel case

Published online by Cambridge University Press:  01 May 1999

ARIANE MÉZARD
ARIANE MÉZARD
Affiliation:
Institut Fourier, Université de Grenoble 1, UMR 5582 CNRS-UJF 38402 Saint-Martin d'Hères, France; e-mail: mezard@ujf-grenoble.fr
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Abstract

We compute the (uni)versal deformation ring of an odd Galois representation ρ: Gal (M/Q) → Gl2(Fp) with an upper triangular image, where M is the maximal abelian pro-p-extension of F∞ unramified outside a finite set of places S, F∞ being a free pro-p-extension of a subextension F of the field K fixed by Ker ρ. We establish a link between the latter (uni)versal deformation ring and the (uni)versal deformation ring of ρ: Gal (KS/Q) → Gl2(Fp), where KS is the maximal pro-p-extension of K unramified outside S. We then give some examples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 126 , Issue 3 , May 1999 , pp. 417 - 442
Copyright
The Cambridge Philosophical Society 1999

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