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An analogue of the field-of-norms functor and of the Grothendieck Conjecture.

Abrashkin, V. (2007) 'An analogue of the field-of-norms functor and of the Grothendieck Conjecture.', Journal of algebraic geometry., 16 (4). pp. 671-730.

Abstract

The paper contains a construction of an analogue of the Fontaine-Wintenberger field-of-norms functor for higher-dimensional local fields. This construction is done completely in terms of the ramification theory of such fields. It is applied to deduce the mixed characteristic case of a local analogue of the Grothendieck conjecture for these fields from its characteristic $ p$ case, which was proved earlier by the author.

Item Type:Article
Keywords:Anabelian conjecture, Ramification filtration, Higher dimensional local fields.
Full text:PDF - Published Version (541Kb)
Status:Peer-reviewed
Publisher Web site:http://www.ams.org/distribution/jag/2007-16-04/S1056-3911-07-00470-5/home.html
Publisher statement:First published in Journal of algebraic geometry, 16 (4) 2007, published by the American Mathematical Society
Record Created:27 Aug 2008
Last Modified:06 Sep 2011 16:34

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