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International Mathematics Research Notices (2000) 2000:1213-1223, doi:10.1155/S107379280000060X
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

The local correspondence over absolute fields: an algebraic approach

Ido Efrat

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.


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