# An application of a theorem of Emerton to mod $p$ representations of $\mathrm{GL}_2$

Abstract : Let $p$ be a prime and $L$ be a finite extension of $\mathbb{Q}_p$. We study the ordinary parts of $\mathrm{GL}_2(L)$-representations arised in the mod $p$ cohomology of Shimura curves attached to indefinite division algebras which splits at a finite place above $p$. The main tool of the proof is a theorem of Emerton \cite{Em3}.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01281383
Contributor : Marie-Annick Guillemer <>
Submitted on : Wednesday, March 2, 2016 - 9:58:23 AM
Last modification on : Friday, November 16, 2018 - 1:23:13 AM

### Citation

Yongquan Hu. An application of a theorem of Emerton to mod $p$ representations of $\mathrm{GL}_2$. Journal of the London Mathematical Society, London Mathematical Society, 2017, 96 (3), pp.545-564. ⟨10.1112/jlms.12080⟩. ⟨hal-01281383⟩

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