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

TL;DR

The paper introduces a geometric approach to measure wild ramification of l-adic sheaves and defines their characteristic cycle, linking ramification data to intersection theory and Euler characteristics.

Contribution

It develops a new geometric method for analyzing wild ramification and defines the characteristic cycle of l-adic sheaves as a cycle on the logarithmic cotangent bundle.

Findings

The method quantifies wild ramification along boundaries.

The characteristic cycle is linked to the characteristic class and Euler number.

The approach generalizes previous ramification measures.

Abstract

We propose a geometric method to measure the wild ramification of a smooth etale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of positive characteristic with arbitrary residue field. We also define the characteristic cycle of an l-adic sheaf, satisfying certain conditions, as a cycle on the logarithmic cotangent bundle and prove that the intersection with the 0-section computes the characteristic class, and hence the Euler number. Definition 2.1.1 is corrected in v2.