Eisenstein Deformation Rings

Frank Calegari

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Eisenstein Deformation Rings

Frank Calegari

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Abstract

We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we determine (using the theory of Breuil modules) when two finite flat group schemes G and H of order p over an arbitrarily tamely ramified discrete valuation ring admit an extension not killed by p.

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Frank Calegari. 2005-03-17. Eisenstein Deformation Rings. https://arxiv.org/abs/math/0407003

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