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

Abrashkin, Victor

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


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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.

Citation

Abrashkin, V. (2007). An analogue of the field-of-norms functor and of the Grothendieck Conjecture. Journal of Algebraic Geometry, 16(4), 671-730. https://doi.org/10.1090/s1056-3911-07-00470-5

Journal Article Type Article
Publication Date Aug 1, 2007
Deposit Date Aug 27, 2008
Publicly Available Date Mar 28, 2024
Journal Journal of Algebraic Geometry
Print ISSN 1056-3911
Electronic ISSN 1534-7486
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 16
Issue 4
Pages 671-730
DOI https://doi.org/10.1090/s1056-3911-07-00470-5
Keywords Anabelian conjecture, Ramification filtration, Higher dimensional local fields.
Publisher URL http://www.ams.org/distribution/jag/2007-16-04/S1056-3911-07-00470-5/home.html

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Copyright Statement
First published in Journal of algebraic geometry, 16 (4) 2007, published by the American Mathematical Society




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