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ISSN 1947-6221(e) ISSN 0065-9266(p)

Towards a modulo Langlands correspondence for ${\mathrm{GL}}_2$

Authors: Christophe Breuil and Vytautas Paškūnas
Journal: Memoirs of the AMS 216 (2012)
MSC (2000): Primary 22E50, 11F80, 11F70
Posted: May 23, 2011
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Abstract: We construct new families of smooth admissible $\overline{\mathbb{F}}_p$ -representations of $\mathrm{GL}_2(F)$ , where is a finite extension of $\mathbb{Q}_p$ . When 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 Langlands correspondence.

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