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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2507.06816 |
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| _version_ | 1866909681476173824 |
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| author | Arkhipov, Sergei I. Bondarko, Mikhail V. |
| author_facet | Arkhipov, Sergei I. Bondarko, Mikhail V. |
| contents | We establish new general etale versions of theorems of Barth and Sommese. Respectively, we compute the lower etale cohomology of closed subvarieties of $P^N$ of small codimensions and of their preimages with respect to proper morphisms (that are not necessarily finite; this statement is completely new), and also of the zero loci of sections of ample vector bundles; all these statements are valid over fields of arbitrary characteristics. To obtain these results, we use a new 'fat hyperplane section' Weak Lefschetz-type theorem for etale cohomology of non-projective varieties that is related to a result of Goresky and MacPherson (over complex numbers). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some general étale Weak Lefschetz-type theorems Arkhipov, Sergei I. Bondarko, Mikhail V. Algebraic Geometry K-Theory and Homology Primary 14F20 14G17, secondary 14M10 19F27 16E10 13B40, 18F20, 55R25 We establish new general etale versions of theorems of Barth and Sommese. Respectively, we compute the lower etale cohomology of closed subvarieties of $P^N$ of small codimensions and of their preimages with respect to proper morphisms (that are not necessarily finite; this statement is completely new), and also of the zero loci of sections of ample vector bundles; all these statements are valid over fields of arbitrary characteristics. To obtain these results, we use a new 'fat hyperplane section' Weak Lefschetz-type theorem for etale cohomology of non-projective varieties that is related to a result of Goresky and MacPherson (over complex numbers). |
| title | Some general étale Weak Lefschetz-type theorems |
| topic | Algebraic Geometry K-Theory and Homology Primary 14F20 14G17, secondary 14M10 19F27 16E10 13B40, 18F20, 55R25 |
| url | https://arxiv.org/abs/2507.06816 |