Publication details for Victor AbrashkinAbrashkin, Victor (2007). An analogue of the field-of-norms functor and of the Grothendieck Conjecture. Journal of Algebraic Geometry 16(4): 671-730.
- Publication type: Journal Article
- ISSN/ISBN: 1056-3911, 1534-7486
- DOI: 10.1090/S1056-3911-07-00470-5
- Keywords: anabelian conjecture, ramification filtration, higher dimensional local fields
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.