A finiteness result on representations of Nori's fundamental group scheme
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866915948134400000 |
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| author | Yi, Xiaodong |
| author_facet | Yi, Xiaodong |
| contents | Let $(X,x)$ be a pointed geometrically connected smooth projective variety over a sub-$p$-adic field $K$. For any given rank $n$, we prove that there are only finitely many isomorphism classes of representations $π_{1}^{EF}(X,x)\rightarrow \mathrm{GL}_{n}$, where $π_{1}^{EF}(X,x)$ is Nori's fundamental group of essentially finite bundles. Equivalently, there are only finitely many isomorphism classes of essentially finite bundles of rank $n$. This answers a question from C.Gasbarri. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13917 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A finiteness result on representations of Nori's fundamental group scheme Yi, Xiaodong Algebraic Geometry Let $(X,x)$ be a pointed geometrically connected smooth projective variety over a sub-$p$-adic field $K$. For any given rank $n$, we prove that there are only finitely many isomorphism classes of representations $π_{1}^{EF}(X,x)\rightarrow \mathrm{GL}_{n}$, where $π_{1}^{EF}(X,x)$ is Nori's fundamental group of essentially finite bundles. Equivalently, there are only finitely many isomorphism classes of essentially finite bundles of rank $n$. This answers a question from C.Gasbarri. |
| title | A finiteness result on representations of Nori's fundamental group scheme |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.13917 |