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Constructing Galois Representations with Very Large Image
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- 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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- Article
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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 $p$.
