David Savitt
Published 2004-04-19, updated 2010-09-15Version 3
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 Mezard (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.
Comments: This version seamlessly folds in the erratum that can be found separately as Appendix A of http://arxiv.org/pdf/0909.1278. Main results are unchanged and theorem numbering is consistent with that of the published version
Journal: Duke Math. Journal 128 (2005), no. 1, 141-197
On a conjecture of Wilf
On a conjecture of Dekking : The sum of digits of even numbers
A Conjecture Connected with Units of Quadratic Fields
![QR code for arXiv:math/0404327 [math.NT]](http://oss.arxitics.com/images/favicon.svg)