• Corpus ID: 221818751

# On the mod $p$ cohomology for $\mathrm{GL}_2$: the non-semisimple case

@article{Hu2020OnTM,
title={On the mod \$p\$ cohomology for \$\mathrm\{GL\}\_2\$: the non-semisimple case},
author={Yong Hu and Haoran Wang},
journal={arXiv: Number Theory},
year={2020}
}
• Published 21 September 2020
• Mathematics
• arXiv: Number Theory
Let $F$ be a totally real field unramified at all places above $p$ and $D$ be a quaternion algebra which splits at either none, or exactly one, of the infinite places. Let $\overline{r}:\mathrm{Gal}(\overline{F}/F)\rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a continuous irreducible representation which, when restricted to a fixed place $v|p$, is non-semisimple and sufficiently generic. Under some mild assumptions, we prove that the admissible smooth representations of $\mathrm{GL}_2… ## References SHOWING 1-10 OF 69 REFERENCES Multiplicity one for wildly ramified representations • Daniel Le • Mathematics Algebra & Number Theory • 2019 Let$F$be a totally real field in which$p$is unramified. Let$\overline{r}: G_F \rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$be a modular Galois representation which satisfies the On the weights of mod p Hilbert modular forms We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod p Hilbert modular forms, by making use of modularity lifting theorems and computations in p-adic Diagrams in the mod p cohomology of Shimura curves • Mathematics Compositio Mathematica • 2021 Abstract We prove a local–global compatibility result in the mod$p$Langlands program for$\mathrm {GL}_2(\mathbf {Q}_{p^f})$. Namely, given a global residual representation$\bar {r}\$ appearing in
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• 2020
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