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1 results

Constructing Galois Representations with Very Large Image
Ravi Ramakrishna
Journal:

Canadian Journal of Mathematics / Volume 60 / Issue 1 / 01 February 2008

Published online by Cambridge University Press:

20 November 2018, pp. 208-221

Print publication:

01 February 2008
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Starting with a 2-dimensional mod $p$ Galois representation, we construct a deformation to a power series ring in infinitely many variables over the $p$-adics. The image of this representation is full in the sense that it contains $S{{L}_{2}}$ of this power series ring. Furthermore, all ${{\mathbb{Z}}_{p}}$ specializations of this deformation are potentially semistable at $p$.