Gelfand-Kirillov dimension and mod p cohomology for GL2
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929335664902144 |
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| author | Breuil, Christophe Herzig, Florian Hu, Yongquan Morra, Stefano Schraen, Benjamin |
| author_facet | Breuil, Christophe Herzig, Florian Hu, Yongquan Morra, Stefano Schraen, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_03127 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Gelfand-Kirillov dimension and mod p cohomology for GL2 Breuil, Christophe Herzig, Florian Hu, Yongquan Morra, Stefano Schraen, Benjamin Number Theory Representation Theory 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. |
| title | Gelfand-Kirillov dimension and mod p cohomology for GL2 |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2009.03127 |