The Local Correspondence over Absolute Fields: An Algebraic Approach

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2 Scopus citations

Abstract

Let K,K′ be infinite fields which are finitely generated over their prime fields. Pop proved using model-theoretic methods that any isomorphism of the absolute Galois groups of K and K′ maps the decomposition groups of the Zariski prime divisors on K bijectively onto the decomposition groups of the Zariski prime divisors on K′ (relative to the separable closures). This was a main ingredient in his proof of the 0-dimensional case of Grothendieck's anabelian conjecture. In this paper we give a simplified and purely algebraic proof of this fact.
Original languageEnglish
Pages (from-to)1213–1223
JournalInternational Mathematics Research Notices
Volume2000
Issue number23
DOIs
StatePublished - 1 Dec 2000

ASJC Scopus subject areas

  • General Mathematics

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