Gelfand-Kirillov dimension and mod p cohomology for GL2
| Autor: | Breuil, Christophe, Herzig, Florian, Hu, Yongquan, Morra, Stefano, Schraen, Benjamin |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Invent. Math. 234 (2023), no. 1, 1-128 |
| Druh dokumentu: | Working Paper |
| Popis: | Let $p$ be a prime number, $F$ a totally real number field unramified at places above $p$ and $D$ a quaternion algebra of center $F$ split at places above $p$ and at no more than one infinite place. Let $v$ be a fixed place of $F$ above $p$ and $\overline{r} : {\rm Gal}(\overline F/F)\rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ an irreducible modular continuous Galois representation which, at the place $v$, is semisimple and sufficiently generic (and satisfies some weak genericity conditions at a few other finite places). We prove that many of the admissible smooth representations of $\mathrm{GL}_2(F_v)$ over $\overline{\mathbb{F}}_p$ associated to $\overline{r}$ in the corresponding Hecke-eigenspaces of the mod $p$ cohomology have Gelfand--Kirillov dimension $[F_v:\mathbb{Q}]$, as well as several related results. Comment: Final version, to appear in Inventiones Mathematicae |
| Databáze: | arXiv |
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