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arXiv · 2309.05398

Characterising local fields of positive characteristic by Galois theory and the Brauer group

Philip Dittmann
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Abstract

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 $p$.

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Philip Dittmann. 2023-09-11. Characterising local fields of positive characteristic by Galois theory and the Brauer group. https://doi.org/10.1112/s0010437x25102364

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