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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Victor Abrashkin

Abrashkin, Victor (2010). Modified proof of a local analogue of the Grothendieck Conjecture. Journal Theorie des Nombres de Bordeaux 22(1): 1-50.

Author(s) from Durham


A local analogue of the Grothendieck Conjecture is an equivalence of the category of complete discrete valuation fields K with finite residue fields of characteristic p and the category of their Galois groups together with their ramification filtration. The case of field of characteristic 0 was considered earlier by Mochizuki, the the author proved it by differennt method if p>2, but the characteristic of K is not necessarily 0. This paper represents a modified approach, which covers also the case p=2.