The Breuil-Mézard conjecture for non-scalar split residual representations

The Breuil–mézard Conjecture for Potentially Barsotti–tate Representations

We prove the Breuil–Mézard conjecture for 2-dimensional potentially Barsotti–Tate representations of the absolute Galois group GK , K a finite extension of Qp, for any p > 2 (up to the question of determining precise values for the multiplicities that occur). In the case that K/Qp is unramified, we also determine most of the multiplicities. We then apply these results to the weight part of Serr...

The Fontaine-mazur Conjecture for Gl2

Introduction 641 1. Breuil-Mézard conjecture and the p-adic local Langlands 644 (1.1) The Breuil-Mézard conjecture 644 (1.2) Review of Colmez’s functor 647 (1.3) Hilbert-Samuel multiplicities 650 (1.4) Representations and pseudo-representations 653 (1.5) GL2(Qp)-representations mod p. 657 (1.6) Local patching and multiplicities 661 (1.7) From pseudo-representations to representations 669 2. Mod...

The Breuil–mézard Conjecture for Quaternion Algebras

We formulate a version of the Breuil–Mézard conjecture for quaternion algebras, and show that it follows from the Breuil–Mézard conjecture for GL2. In the course of the proof we establish a mod p analogue of the Jacquet– Langlands correspondence for representations of GL2(k), k a finite field of characteristic p.

The Breuil–mézard Conjecture for Potentially Barsotti–tate Representations. Toby Gee and Mark Kisin

We prove the Breuil–Mézard conjecture for 2-dimensional potentially Barsotti–Tate representations of the absolute Galois group GK , K a finite extension of Qp, for any p > 2 (up to the question of determining precise values for the multiplicities that occur). In the case that K/Qp is unramified, we also determine most of the multiplicities. We then apply these results to the weight part of Serr...

On Lattices in Semi-stable Representations: a Proof of a Conjecture of Breuil