ON A LOCAL ANALOGUE OF THE GROTHENDIECK CONJECTURE

Abstract

We prove that the functor from the category of all complete discrete valuation fields with finite residue fields of characteristic ≠2 to the category of profinite filtered groups given by taking the Galois group of corresponding field together with its filtration by higher ramification subgroups is fully faithful. If [K; ℚp]<∞ we also study the opportunity to recover K from the knowledge of the filtered group ΓK(p)/ΓK(p)(a), where a>0, ΓK(p) is the absolute Galois group of the maximal p-extension of K and filtration is induced by ramification filtration.