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.
Abrashkin, V. (2010). Modified proof of a local analogue of the Grothendieck Conjecture. Journal de théorie des nombres de Bordeaux, 22(1), 1-50. https://doi.org/10.5802/jtnb.703