Non-finite type étale sites over fields
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908321311621120 |
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| author | Dhamore, Sujeet Hogadi, Amit Pawar, Rakesh |
| author_facet | Dhamore, Sujeet Hogadi, Amit Pawar, Rakesh |
| contents | We consider the notion of finite type-ness of a site introduced by Morel and Voevodsky, for the étale site of a field. For a given field $k$, we conjecture that the étale site of $Sm/k$ is of finite type if and only if the field $k$ admits a finite extension of finite cohomological dimension. We prove this conjecture in some cases, e.g. in the case when $k$ is countable, or in the case when the $p$-cohomological dimension $cd_p(k)$ is infinite for infinitely many primes $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-finite type étale sites over fields Dhamore, Sujeet Hogadi, Amit Pawar, Rakesh Algebraic Geometry 14F20, 14F35, 14F42 (Primary), 12G05, 12G10 (Secondary) We consider the notion of finite type-ness of a site introduced by Morel and Voevodsky, for the étale site of a field. For a given field $k$, we conjecture that the étale site of $Sm/k$ is of finite type if and only if the field $k$ admits a finite extension of finite cohomological dimension. We prove this conjecture in some cases, e.g. in the case when $k$ is countable, or in the case when the $p$-cohomological dimension $cd_p(k)$ is infinite for infinitely many primes $p$. |
| title | Non-finite type étale sites over fields |
| topic | Algebraic Geometry 14F20, 14F35, 14F42 (Primary), 12G05, 12G10 (Secondary) |
| url | https://arxiv.org/abs/2405.06612 |