Tame and curve-tame cohomology of $\mathbb A^1$-invariant étale sheaves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911228526329856 |
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| author | S, Sandeep Sawant, Anand |
| author_facet | S, Sandeep Sawant, Anand |
| contents | We extend the definition of the unramified curve-tame cohomology groups to $\mathbb{A}^1$-invariant étale sheaves under some additional hypotheses. We define a pairing of this group with the Suslin homology satisfying desirable properties and using this, we show that the unramified curve-tame cohomology of a smooth geometrically connected variety over a field of positive characteristic agrees with the cohomology of the base field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tame and curve-tame cohomology of $\mathbb A^1$-invariant étale sheaves S, Sandeep Sawant, Anand Algebraic Geometry K-Theory and Homology 14C25, 14C35, 19E15 We extend the definition of the unramified curve-tame cohomology groups to $\mathbb{A}^1$-invariant étale sheaves under some additional hypotheses. We define a pairing of this group with the Suslin homology satisfying desirable properties and using this, we show that the unramified curve-tame cohomology of a smooth geometrically connected variety over a field of positive characteristic agrees with the cohomology of the base field. |
| title | Tame and curve-tame cohomology of $\mathbb A^1$-invariant étale sheaves |
| topic | Algebraic Geometry K-Theory and Homology 14C25, 14C35, 19E15 |
| url | https://arxiv.org/abs/2403.01735 |