Computation of a universal deformation ring

Details Computation of a universal deformation ring Computation of a universal deformation ring

1998-06-08

arxiv.org/abs/math/9806169v1

Mathematics

Number Theory

Scientific paper

10.1017/S0305004198003399

We compute the universal deformation ring of an odd Galois two dimensional representation of Gal$(M/Q)$ with an upper triangular image, where $M$ is the maximal abelian pro-$p$-extension of $F_{\infty}$ unramified outside a finite set of places S, $F_{\infty}$ being a free pro-$p$-extension of a subextension $F$ of the field $K$ fixed by the kernel of the representation. We establish a link between the latter universal deformation ring and the universal deformation ring of the representation of Gal$(K_S/Q)$, where $K_S$ is the maximal pro-$p$-extension of $K$ unramified outside $S$. We then give some examples. This paper was accepted for publication in the Mathematical Proceedings of the Cambridge philosophical society (May 99).

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