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

Abrashkin, Victor

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: Aug 27, 2008
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1538854
• Publisher URL: http://www.ams.org/distribution/jag/2007-16-04/S1056-3911-07-00470-5/home.html