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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Victor Abrashkin

Abrashkin, Victor (2007). An analogue of the field-of-norms functor and of the Grothendieck Conjecture. Journal of Algebraic Geometry 16(4): 671-730.

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.