Eisenstein Deformation Rings

Details Eisenstein Deformation Rings Eisenstein Deformation Rings

2004-06-30

arxiv.org/abs/math/0407003v2

Mathematics

Number Theory

final version

Scientific paper

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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