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Constructing Galois Representations with Very Large Image

Open Access article
 Printed: Feb 2008
  • Ravi Ramakrishna
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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 $\SL_2$ of this power series ring. Furthermore, all ${\mathbb Z}_p$ specializations of this deformation are potentially semistable at $p$.
Keywords: Galois representation, deformation Galois representation, deformation
MSC Classifications: 11f80 show english descriptions unknown classification 11f80 11f80 - unknown classification 11f80

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