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Eisenstein deformation rings

Published online by Cambridge University Press:  13 January 2006

Frank Calegari
Frank Calegari
Affiliation:
Department of Mathematics, Harvard University, 432 Science Center, 1 Oxford Street, Cambridge, MA 02138, [email protected]
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Abstract

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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.

Keywords

Galois representationsmodular forms11F80
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 1 , January 2006 , pp. 63 - 83
Copyright
Foundation Compositio Mathematica 2006