Kato-Milne cohomology group over rational function fields in characteristic 2, I
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917964520882176 |
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| author | Laghribi, Ahmed Maiti, Trisha |
| author_facet | Laghribi, Ahmed Maiti, Trisha |
| contents | Let F be a field of characteristic 2. In this paper we determine the Kato-Milne cohomology of the rational function field F(x) in one variable x. This will be done by proving an analogue of the Milnor exact sequence [4] in the setting of Kato-Milne cohomology. As an application, we answer the open case of the norm theorem for Kato-Milne cohomology that concerns separable irreducible polynomials in many variables. This completes a result of Mukhija [17, Theorem A.3] that gives the norm theorem for inseparable polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kato-Milne cohomology group over rational function fields in characteristic 2, I Laghribi, Ahmed Maiti, Trisha Commutative Algebra 11E04, 11E81, 13N05 Let F be a field of characteristic 2. In this paper we determine the Kato-Milne cohomology of the rational function field F(x) in one variable x. This will be done by proving an analogue of the Milnor exact sequence [4] in the setting of Kato-Milne cohomology. As an application, we answer the open case of the norm theorem for Kato-Milne cohomology that concerns separable irreducible polynomials in many variables. This completes a result of Mukhija [17, Theorem A.3] that gives the norm theorem for inseparable polynomials. |
| title | Kato-Milne cohomology group over rational function fields in characteristic 2, I |
| topic | Commutative Algebra 11E04, 11E81, 13N05 |
| url | https://arxiv.org/abs/2503.16859 |