Is there a group structure on the Galois cohomology of a reductive group over a global field?
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913733346852864 |
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| author | Borovoi, Mikhail |
| author_facet | Borovoi, Mikhail |
| contents | Let K be a global field, that is, a number field or a global function field. It is known that the answer to the question in the title over K is "Yes" when K has no real embeddings. We show that otherwise the answer is "No". Namely, we show that when K is a number field admitting a real embedding, it is impossible to define a group structure on the first Galois cohomology sets H^1(K,G) for all reductive K-groups G in a functorial way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Is there a group structure on the Galois cohomology of a reductive group over a global field? Borovoi, Mikhail Number Theory Algebraic Geometry Group Theory 11E72, 20G10, 20G20, 20G30 Let K be a global field, that is, a number field or a global function field. It is known that the answer to the question in the title over K is "Yes" when K has no real embeddings. We show that otherwise the answer is "No". Namely, we show that when K is a number field admitting a real embedding, it is impossible to define a group structure on the first Galois cohomology sets H^1(K,G) for all reductive K-groups G in a functorial way. |
| title | Is there a group structure on the Galois cohomology of a reductive group over a global field? |
| topic | Number Theory Algebraic Geometry Group Theory 11E72, 20G10, 20G20, 20G30 |
| url | https://arxiv.org/abs/2408.16783 |