Ramification filtration and differential forms

Abstract

Let K = k 0 ((t 0 )) where [k 0 : F p ] < ∞. Denote by K tr the maximal tamely ramified extension of K in K sep and letsatisfying the following condition. Suppose F = r∈Q t −r 0 l r , where all l r ∈ L(H) ⊗ Fp . For v > 0, consider the minimal ideal L(H) (v) in L(H) such that L(H) (v) ⊗ Fp contains all l r wirh r v. Then the image of the ramification subgroup in the upper numbering ΓThe form ω(H) is defined in terms of the matrices of Frobenius and connection on the φ-module associated with H. In the end of paper we sketch how the same result can be obtained for arbitrary Z p [Γ K ]-modules.