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arXiv · 1109.4226

A geometric perspective on the Breuil-Mézard conjecture

Matthew Emerton·Toby Gee
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Abstract

Let p > 2 be prime. We state and prove (under mild hypotheses on the residual representation) a geometric refinement of the Breuil-Mézard conjecture for 2-dimensional mod p representations of the absolute Galois group of Qp. We also state a conjectural generalisation to n-dimensional representations of the absolute Galois group of an arbitrary finite extension of Qp, and give a conditional proof of this conjecture, subject to a certain R = T-type theorem together with a strong version of the weight part of Serre's conjecture for rank n unitary groups. We deduce an unconditional result in the case of two-dimensional potentially Barsotti-Tate representations.

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Matthew Emerton, Toby Gee. 2013-03-20. A geometric perspective on the Breuil-Mézard conjecture. https://arxiv.org/abs/1109.4226

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