Geometry & Topology Monographs 3 (2000) - Invitation to higher local fields, Part II, section 7, pages 273-279

Recovering higher global and local fields from Galois groups - an algebraic approach

I. Efrat

Abstract. A main problem in Galois theory is to characterize the fields with a given absolute Galois group. We apply a K-theoretic method for constructing valuations to study this problem in various situations. As a first application we obtain an algebraic proof of the 0-dimensional case of Grothendieck's anabelian conjecture (proven by Pop), which says that finitely generated infinite fields are determined up to purely inseparable extensions by their absolute Galois groups. As a second application (which is a joint work with Fesenko) we analyze the arithmetic structure of fields with the same absolute Galois group as a higher-dimensional local field.
Keywords. Field arithmetic, henselian valuations, higher local fields.
AMS subject classification. 12E30, 12J25, 19M05.

E-print: arXiv:math.NT/0012157

Ido Efrat
Department of Mathematics, Ben Gurion University of the Negev, P.O.Box 653, Be'er-Sheva, 84105 Israel

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