Functorial splitting of $l$-adic cohomology in exact sequences of group varieties
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910420439138304 |
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| author | de Vries, Victor |
| author_facet | de Vries, Victor |
| contents | In this document we consider an exact sequence of group varieties $e\to N\to G\to Q\to e$ over an algebraically closed field. We show that for $l\neq \mathrm{char}(k)$ a prime there exists an isomorphism of graded $\mathbb{Q}_l$-algebras $\mathrm{H}_{\text{ét}}^*(G,\mathbb{Q}_l)\cong \mathrm{H}_{\text{ét}}^*(N,\mathbb{Q}_l)\otimes_{\mathbb{Q}_l}\mathrm{H}_{\text{ét}}^*(Q,\mathbb{Q}_l)$ that is compatible with pullback homomorphisms $f^*$ of endomorphisms $f:G\to G$ that stabilize $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Functorial splitting of $l$-adic cohomology in exact sequences of group varieties de Vries, Victor Algebraic Geometry In this document we consider an exact sequence of group varieties $e\to N\to G\to Q\to e$ over an algebraically closed field. We show that for $l\neq \mathrm{char}(k)$ a prime there exists an isomorphism of graded $\mathbb{Q}_l$-algebras $\mathrm{H}_{\text{ét}}^*(G,\mathbb{Q}_l)\cong \mathrm{H}_{\text{ét}}^*(N,\mathbb{Q}_l)\otimes_{\mathbb{Q}_l}\mathrm{H}_{\text{ét}}^*(Q,\mathbb{Q}_l)$ that is compatible with pullback homomorphisms $f^*$ of endomorphisms $f:G\to G$ that stabilize $N$. |
| title | Functorial splitting of $l$-adic cohomology in exact sequences of group varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.03501 |