On a conjecture of Conrad, Diamond, and Taylor

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46 Scopus citations

Abstract

We prove a conjecture of Conrad, Diamond, and Taylor on the size of certain deformation rings parametrizing potentially Barsotti-Tate Galois representations. To achieve this, we extend results of Breuil and Mézard (classifying Galois lattices in semistable representations in terms of "strongly divisible modules") to the potentially crystalline case in Hodge-Tote weights (0,1). We then use these strongly divisible modules to compute the desired deformation rings. As a corollary, we obtain new results on the modularity of potentially Barsotti-Tate representations.

Original languageEnglish (US)
Pages (from-to)141-197
Number of pages57
JournalDuke Mathematical Journal
Volume128
Issue number1
DOIs
StatePublished - May 15 2005

ASJC Scopus subject areas

  • Mathematics(all)

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