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# memo_has_moved_text();Towards a modulo $p$ Langlands correspondence for $\mathrm {GL}_{2}$

Christophe Breuil, C.N.R.S. & I.H.É.S., Le Bois-Marie, 35 route de Chartres, 91440 Bures-sur-Yvette, France and Vytautas Paškūnas, Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

Publication: Memoirs of the American Mathematical Society
Publication Year: 2012; Volume 216, Number 1016
ISBNs: 978-0-8218-5227-9 (print); 978-0-8218-8525-3 (online)
DOI: http://dx.doi.org/10.1090/S0065-9266-2011-00623-4
Published electronically: May 23, 2011
Keywords:Supersingular, $mod p$ Langlands correspondence, Serre weights
MSC: Primary 22E50, 11F80, 11F70

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Chapters

• Chapter 1. Introduction
• Chapter 2. Representation theory of $\Gamma$ over $\bar {\mathbb {F}}_p$ I
• Chapter 3. Representation theory of $\Gamma$ over $\bar {\mathbb {F}}_p$ II
• Chapter 4. Representation theory of $\Gamma$ over $\bar {\mathbb {F}}_p$ III
• Chapter 5. Results on $K$-extensions
• Chapter 6. Hecke algebra
• Chapter 7. Computation of $\mathbb {R}^1 \mathcal {I}$ for principal series
• Chapter 8. Extensions of principal series
• Chapter 9. General theory of diagrams and representations of $\mathrm {GL}_2$
• Chapter 10. Examples of diagrams
• Chapter 11. Generic Diamond weights
• Chapter 12. The unicity Lemma
• Chapter 13. Generic Diamond diagrams
• Chapter 14. The representations $D_0(\rho )$ and $D_1(\rho )$
• Chapter 15. Decomposition of generic Diamond diagrams
• Chapter 16. Generic Diamond diagrams for $f \in \{1,2\}$
• Chapter 17. The representation $R(\sigma )$
• Chapter 18. The extension lemma
• Chapter 19. Generic Diamond diagrams and representations of $\mathrm {GL}_2$
• Chapter 20. The case $F = \mathbb {Q}_p$

### Abstract

We construct new families of smooth admissible $\overline {\mathbb {F}}_p$-representations of $\mathrm {GL}_2(F)$, where $F$ is a finite extension of $\mathbb {Q}_p$. When $F$ is unramified, these representations have the $\mathrm {GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. Our motivation is a hypothetical mod $p$ Langlands correspondence.

### References [Enhancements On Off] (What's this?)

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