On a Conjecture I for unirational algebraic groups over an imperfect field
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908941332512768 |
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| author | Lourdeaux, Alexandre Zidani, Anis |
| author_facet | Lourdeaux, Alexandre Zidani, Anis |
| contents | Using the recent advancements in the structure of algebraic groups over imperfect fields, we propose a generalization of Serre's Conjecture I and of results that revolve around it. In particular, we prove that the first Galois cohomology set of any unirational algebraic group is always trivial if the cohomological dimension of the field is less or equal to 1 in Kato's sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05148 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Conjecture I for unirational algebraic groups over an imperfect field Lourdeaux, Alexandre Zidani, Anis Algebraic Geometry 11E72, 20G15 (primary), 20G07 (secondary) Using the recent advancements in the structure of algebraic groups over imperfect fields, we propose a generalization of Serre's Conjecture I and of results that revolve around it. In particular, we prove that the first Galois cohomology set of any unirational algebraic group is always trivial if the cohomological dimension of the field is less or equal to 1 in Kato's sense. |
| title | On a Conjecture I for unirational algebraic groups over an imperfect field |
| topic | Algebraic Geometry 11E72, 20G15 (primary), 20G07 (secondary) |
| url | https://arxiv.org/abs/2604.05148 |