|November 14, 2023||
Characterising local fields by mostly Galois-theoretic dataPhilip Dittmann, TU Dresden, Germany RIMS Kyoto + Zoom · JP:16:30 · FR:08:30
Some of the fundamental problems of anabelian geometry are related to characterising fields by Galois-theoretic data. Old results here include axiomatisations of individual fields within certain classes (such as axiomatising global fields by their absolute Galois groups as in the Neukirch-Uchida Theorem) as well as, more importantly for us, the Galois-theoretic characterisation of the so-called p-adically closed fields (a class encompassing the finite extensions of the p-adic numbers) among all fields.
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