Gelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917414151651328 |
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| author | Dotto, Andrea Hung, Bao V. Le |
| author_facet | Dotto, Andrea Hung, Bao V. Le |
| contents | Under standard assumptions, we compute the GK-dimension of Hecke eigenspaces in the mod $p$ cohomology of an inner form $D^\times$ of $\mathrm{GL}_2$ over a totally real field unramified at $p$, allowing $D$ to be a division algebra at $p$. Our arguments also apply when $D$ is a matrix algebra at $p$, in which case they give a simplified proof of a theorem of Breuil--Herzig--Hu--Morra--Schraen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$ Dotto, Andrea Hung, Bao V. Le Number Theory Representation Theory Under standard assumptions, we compute the GK-dimension of Hecke eigenspaces in the mod $p$ cohomology of an inner form $D^\times$ of $\mathrm{GL}_2$ over a totally real field unramified at $p$, allowing $D$ to be a division algebra at $p$. Our arguments also apply when $D$ is a matrix algebra at $p$, in which case they give a simplified proof of a theorem of Breuil--Herzig--Hu--Morra--Schraen. |
| title | Gelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2604.15164 |