Characterising local fields of positive characteristic by Galois theory and the Brauer group
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912646248267776 |
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| author | Dittmann, Philip |
| author_facet | Dittmann, Philip |
| contents | We show that each local field $\mathbb{F}_q((t))$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most $1$ by (certain small quotients of) its absolute Galois group together with natural axioms concerning the $p$-torsion of its Brauer group. This complements previous work by Efrat-Fesenko, who analysed fields whose absolute Galois group is isomorphic to that of a local field of characteristic $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05398 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterising local fields of positive characteristic by Galois theory and the Brauer group Dittmann, Philip Number Theory 12F12 (primary) 12J10, 11S70 (secondary) We show that each local field $\mathbb{F}_q((t))$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most $1$ by (certain small quotients of) its absolute Galois group together with natural axioms concerning the $p$-torsion of its Brauer group. This complements previous work by Efrat-Fesenko, who analysed fields whose absolute Galois group is isomorphic to that of a local field of characteristic $p$. |
| title | Characterising local fields of positive characteristic by Galois theory and the Brauer group |
| topic | Number Theory 12F12 (primary) 12J10, 11S70 (secondary) |
| url | https://arxiv.org/abs/2309.05398 |