THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS

By T. Gee, M. Kisin. Forum of Mathematics, Pi, 2012

117 citations recorded by the source corpus.

Abstract We prove the Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate representations of the absolute Galois group $G_{K}$, $K$ a finite extension of $\mathbb{Q}_{p}$, for any $p>2$ (up to the question of determining precise values for the multiplicities that occur). In the case that $K/\mathbb{Q}_{p}$ is unramified, we also determine most of the multiplicities. We then apply these results to the weight part of Serre’s conjecture, proving a variety of results including the Buzzard–Diamond–Jarvis conjecture.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ec7a8c6ece27a61aa87fda3d71e29eba8d4cd202

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In Geometry and Topology

1. T. Gee
2. M. Emerton
3. David Geraghty
4. Vytautas Paškūnas
5. Ana Caraiani
6. Peter Scholze
7. J. Thorne
8. F. Herzig

In Mathematical Physics

1. T. Gee
2. M. Emerton
3. David Geraghty
4. Vytautas Paškūnas
5. Ana Caraiani
6. Peter Scholze
7. J. Thorne
8. F. Herzig

Citations in the corpus

• Patching and the p-adic local Langlands correspondence (2013, background): “ows from Theorem A.4.1 of [BLGG13], which constructs a global automorphic Galois representation corresponding to a point on the same component of R ep(σ)[1/p] as r(cf. the proof of Corollary 4.4.3 of [GK12]). 44 A. CARAIANI, M. EMERTON, T. GEE, D. GERAGHTY, V. PASKˇ UNAS, AND S. W. SHIN¯ Indeed, the”