On Ramification Filtrations and p-adic Differential Equations, I

Let k be a complete discrete valuation field of equal characteristic p > 0 with possibly imperfect residue field. Let Gk be its Galois group. We will prove that the conductors computed by the arithmetic ramification filtrations on Gk defined in [2] coincide with the differential Artin conductors and Swan conductors of Galois representations of Gk defined in [15]. As a consequence, we give a Hasse-Arf theorem for arithmetic ramification filtrations in this case. As an application, we obtain a Hasse-Arf theorem for generically étale finite flat group schemes as stated in [12]. We also give a comparison theorem between the differential Artin conductors and Borger’s conductors [7].