Duke Mathematical Journal

On a conjecture of Conrad, Diamond, and Taylor

David Savitt

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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-Tate 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.

Article information

Source
Duke Math. J., Volume 128, Number 1 (2005), 141-197.

Dates
First available in Project Euclid: 17 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1116361230

Digital Object Identifier
doi:10.1215/S0012-7094-04-12816-7

Mathematical Reviews number (MathSciNet)
MR2137952

Zentralblatt MATH identifier
1101.11017

Subjects
Primary: 11F80: Galois representations
Secondary: 14L15: Group schemes

Citation

Savitt, David. On a conjecture of Conrad, Diamond, and Taylor. Duke Math. J. 128 (2005), no. 1, 141--197. doi:10.1215/S0012-7094-04-12816-7. https://projecteuclid.org/euclid.dmj/1116361230


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