@inbook{281a05e7552742da94e03cd513845e89,

title = "Recovering Higher Global and Local Fields from Galois Groups: An Algebraic Approach",

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 = "math.NT, math.AG, 12E30, 12J25, 19M05",

author = "Ido Efrat",

note = "For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon3/m3-II-7.abs.html Invitation to higher local fields, Part II, section 7",

year = "2000",

month = dec,

doi = "10.2140/gtm.2000.3.273",

language = "English",

volume = "3",

series = "Geometry & Topology Monographs ",

publisher = "Mathematical Sciences Publishers",

pages = "273--279",

booktitle = "Geometry & Topology Monographs 3",

address = "United States",

edition = "Part II section 7",

}