On the Breuil-Mézard conjecture

Abstract

We give a new local proof of Breuil-Mézard conjecture for two dimensional representations of the absolute Galois group of ${\mathbb{Q}}_p$, when $p\ge 5$ and the representation has scalar endomorphisms.

Subsections of §2 have been rearranged; §2.1 (§2.2 in v2) has been rewritten to prove a stronger result; Remark 4.8 in v2 is false, §4 has been rewritten to fix this; Prop.6.23, §8 added

References in corpus (1)

• The Breuil-Mezard conjecture for non-scalar split residual representations

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