Equality of two non-logarithmic ramification filtrations of abelianized Galois group in positive characteristic

TL;DR

This paper proves the equality of two ramification filtrations for abelianized Galois groups in positive characteristic and computes related invariants using sheaves of Witt vectors.

Contribution

It establishes the equality of Matsuda and Abbes-Saito filtrations and computes refined invariants for characters of fundamental groups in positive characteristic.

Findings

Equality of two ramification filtrations proven

Refined Swan conductor computed

Characteristic form of characters determined

Abstract

We prove the equality of two non-logarithmic ramification filtrations defined by Matsuda and Abbes-Saito for the abelianized absolute Galois group of a complete discrete valuation field in positive characteristic. We also compute the refined Swan conductor and the characteristic form of a character of the fundamental group of a smooth separated scheme over a perfect field of positive characteristic by using sheaves of Witt vectors.