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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.03501 |
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Table of 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 $N$.