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Lifting n-Dimensional Galois Representations

Published online by Cambridge University Press:  20 November 2018

Spencer Hamblen
Spencer Hamblen*
Affiliation:
Department of Mathematics and Computer Science, McDaniel College, Westminster, MD, 21157-4390 e-mail:shamblen@mcdaniel.edu
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Abstract

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We investigate the problem of deforming $n$-dimensional mod $p$ Galois representations to characteristic zero. The existence of 2-dimensional deformations has been proven under certain conditions by allowing ramification at additional primes in order to annihilate a dual Selmer group. We use the same general methods to prove the existence of $n$-dimensional deformations.

We then examine under which conditions we may place restrictions on the shape of our deformations at $p$, with the goal of showing that under the correct conditions, the deformations may have locally geometric shape. We also use the existence of these deformations to prove the existence as Galois groups over $\mathbb{Q}$ of certain infinite subgroups of $p$-adic general linear groups.

Keywords

11F80
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 5 , October 2008 , pp. 1028 - 1049
Copyright
Copyright © Canadian Mathematical Society 2008

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