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# Constructing Galois Representations with Very Large Image

Published:2008-02-01
Printed: Feb 2008
• Ravi Ramakrishna
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## Abstract

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 $\SL_2$ of this power series ring. Furthermore, all ${\mathbb Z}_p$ specializations of this deformation are potentially semistable at $p$.
 Keywords: Galois representation, deformation
 MSC Classifications: 11f80 - unknown classification 11f80

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