On singular supports in mixed characteristic
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912336455925760 |
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| author | Saito, Takeshi |
| author_facet | Saito, Takeshi |
| contents | We fix an excellent regular noetherian scheme $S$ over ${\mathbf Z}_{(p)}$ satisfying a certain finiteness condition. For a constructible étale sheaf ${\cal F}$ on a regular scheme $X$ of finite type over $S$, we introduce a variant of the singular support relatively to $S$ and prove the existence of a saturated relative variant of the singular support by adopting the method of Beilinson using the Radon transform. We may deduce the existence of the singular support itself, if we admit an expected property on the micro support of tensor product and if the scheme $X$ is sufficiently ramified over the base $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On singular supports in mixed characteristic Saito, Takeshi Algebraic Geometry 14F20, 11G25 We fix an excellent regular noetherian scheme $S$ over ${\mathbf Z}_{(p)}$ satisfying a certain finiteness condition. For a constructible étale sheaf ${\cal F}$ on a regular scheme $X$ of finite type over $S$, we introduce a variant of the singular support relatively to $S$ and prove the existence of a saturated relative variant of the singular support by adopting the method of Beilinson using the Radon transform. We may deduce the existence of the singular support itself, if we admit an expected property on the micro support of tensor product and if the scheme $X$ is sufficiently ramified over the base $S$. |
| title | On singular supports in mixed characteristic |
| topic | Algebraic Geometry 14F20, 11G25 |
| url | https://arxiv.org/abs/2501.07965 |