Eisenstein deformation rings

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

[学科分类] 数学（综合）