Is there a group structure on the Galois cohomology of a reductive group over a global field?
| Autor: | Borovoi, Mikhail |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 5 pages. This is a part of arXiv:2403.07659 to be published separately |
| Databáze: | arXiv |
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