On a universal deformation ring that is a discrete valuation ring

Abstract: We consider a crystalline universal deformation ring $R$ of an $n$-dimensional, mod $p$ Galois representation whose semisimplification is the direct sum of two non-isomorphic absolutely irreducible representations. Under some hypotheses, we obtain that $R$ is a discrete valuation ring. The method examines the ideal of reducibility of $R$, which is used to construct extensions of representations in a Selmer group with specified dimension. This can be used to deduce modularity of representations.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

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