On ramification filtrations and $p$-adic differential modules, I: equal characteristic case

Abstract

Let $k$ be a complete discretely valued field of equal characteristic $p>0$ with possibly imperfect residue field and let $G_k$ be its Galois group. We prove that the conductors computed by the arithmetic ramification filtrations on $G_k$ coincide with the differential Artin conductors and Swan conductors of Galois representations of $G_k$. As a consequence, we give a Hasse-Arf theorem for arithmetic ramification filtrations in this case. As applications, we obtain a Hasse-Arf theorem for finite flat group schemes; we also give a comparison theorem between the differential Artin conductors and Borger's conductors.

Improvement on some of the proofs following the suggestion of the referee

References in corpus (1)

• Wild ramification and the characteristic cycle of an l-adic sheaf

Cited by in corpus (4)

• An explicit approach to residues on and dualizing sheaves of arithmetic surfaces
• Fubini's theorem and non-linear change of variables over a two-dimensional local field
• On differential modules associated to de Rham representations in the imperfect residue field case
• Euler characteristics, Fubini's theorem, and the Riemann-Hurwitz formula