Lifting $n$-Dimensional Galois Representations
Printed: Oct 2008
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 $\Q$ of certain infinite
subgroups of $p$-adic general linear groups.
11F80 - Galois representations