The $p$-adic Galois Cohomology of Valuation Fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910837484027904 |
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| author | He, Tongmu |
| author_facet | He, Tongmu |
| contents | We compute the Galois cohomology of any $p$-adic valuation field extension of a pre-perfectoid field. Moreover, we obtain a generalization and also a new proof of the classical results of Tate and Hyodo on discrete valuation fields, without using higher ramification group, local class field theory or Epp's elimination of ramifications. A key ingredient is Gabber-Ramero's computation of cotangent complexes for valuation rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $p$-adic Galois Cohomology of Valuation Fields He, Tongmu Algebraic Geometry Commutative Algebra Number Theory 14F30 (primary), 11S25, 13F30 We compute the Galois cohomology of any $p$-adic valuation field extension of a pre-perfectoid field. Moreover, we obtain a generalization and also a new proof of the classical results of Tate and Hyodo on discrete valuation fields, without using higher ramification group, local class field theory or Epp's elimination of ramifications. A key ingredient is Gabber-Ramero's computation of cotangent complexes for valuation rings. |
| title | The $p$-adic Galois Cohomology of Valuation Fields |
| topic | Algebraic Geometry Commutative Algebra Number Theory 14F30 (primary), 11S25, 13F30 |
| url | https://arxiv.org/abs/2502.14858 |