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- W2186520450 abstract "Let $p>5$ be a prime integer and $K/mathbb{Q}_p$ a finite ramified extension with ring of integers $mathcal{O}$ and uniformizer $pi$. Let $n>1$ be a positive integer and $rho_n:G_mathbb{Q} to text{GL}_2(mathcal{O}/pi^n)$ be a continuous Galois representation. In this article we prove that under some technical hypotheses the representation $rho_n$ can be lifted to a representation $rho:G_mathbb{Q} to text{GL}_2(mathcal{O})$. Furthermore, we can pick the lift restriction to inertia at any finite set of primes (at the cost of allowing some extra ramification) and get a deformation problem whose universal ring is isomorphic to $W(mathbb{F})[[X]]$. The lifts constructed are nearly (not necessarily Hodge-Tate) but we can prove the existence of ordinary modular points (up to twist)." @default.
- W2186520450 created "2016-06-24" @default.
- W2186520450 creator A5048451176 @default.
- W2186520450 date "2014-09-08" @default.
- W2186520450 modified "2023-09-27" @default.
- W2186520450 title "Lifting Galois representations to ramified coefficient fields" @default.
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- W2186520450 hasPublicationYear "2014" @default.
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