Characteristic cycle of the exterior product of constructible sheaves

TL;DR

This paper proves that the characteristic cycle of the exterior product of constructible sheaves equals the exterior product of their characteristic cycles, aiding the proof of the index formula.

Contribution

It establishes the compatibility of characteristic cycles with smooth pull-back for constructible complexes, advancing the understanding of their behavior under exterior products.

Findings

Characteristic cycle of exterior product equals exterior product of characteristic cycles

Compatibility of characteristic cycles with smooth pull-back demonstrated

Progress towards proof of the index formula

Abstract

We show that the characteristic cycle of the exterior product of constructible complexes is the exterior product of the characteristic cycles of factors. This implies the compatibility of characteristic cycles with smooth pull-back which is a first step in the proof of the index formula.