Additivity of non-acyclicity classes for constructible \'etale sheaves

TL;DR

This paper develops a categorical trace formula for non-acyclicity classes of constructible étale sheaves and proves their additivity property, advancing the understanding of these classes in algebraic geometry.

Contribution

It introduces a bivariant approach to cohomological correspondences and establishes the additivity of non-acyclicity classes, a novel result in the field.

Findings

Established a trace-like formula for non-acyclicity classes

Proved the additivity property of these classes

Enhanced the theoretical framework for constructible étale sheaves

Abstract

Using a bivariant version of cohomological correspondences, we establish a categorical trace-like formula for the non-acyclicity classes introduced by Yang and Zhao (arXiv:2209.11086). As an application, we prove the additivity for the non-acyclicity classes.