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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.11417 |
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| _version_ | 1866911441497358336 |
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| author | Schoemann, Claudia Werner, Skylar |
| author_facet | Schoemann, Claudia Werner, Skylar |
| contents | Let $k$ be an uncountable algebraically closed field of positive characteristic and let $S$ be a smooth projective connected surface over $k$. We extend the theorem on the Gysin kernel from [20, Theorem 5.1] to also be true over $k$, where it was proved over $\mathbb{C}$. This is done by showing that almost all results still hold true over $k$ via the same argument or by using étale base arguments and then using a lift with the Comparison theorems [16, Theorems 21.1 & 20.5] and Tate's Conjecture for finitely generated fields [27] and [31] as needed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The kernel of the Gysin homomorphism for positive characteristic Schoemann, Claudia Werner, Skylar Algebraic Geometry Let $k$ be an uncountable algebraically closed field of positive characteristic and let $S$ be a smooth projective connected surface over $k$. We extend the theorem on the Gysin kernel from [20, Theorem 5.1] to also be true over $k$, where it was proved over $\mathbb{C}$. This is done by showing that almost all results still hold true over $k$ via the same argument or by using étale base arguments and then using a lift with the Comparison theorems [16, Theorems 21.1 & 20.5] and Tate's Conjecture for finitely generated fields [27] and [31] as needed. |
| title | The kernel of the Gysin homomorphism for positive characteristic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.11417 |