The excess formula in functorial form

TL;DR

This paper refines the excess formula in algebraic K-theory to a functorial level within Deligne's virtual category, providing a unique, property-satisfying construction that enhances understanding of base change failures.

Contribution

It introduces a functorial refinement of the excess formula in algebraic K-theory, establishing its uniqueness and natural properties.

Findings

Existence of a unique excess formula on Deligne's virtual category.

The refined excess formula satisfies a natural set of properties.

Enhances understanding of base change failures in algebraic K-theory.

Abstract

This article is motivated by the need for better understanding of refined Riemann-Roch theorems and the behavior of the determinant of the cohomology. This poses a certain problem of functoriality and can be understood as that of giving refined constructions of operations in algebraic $K$-theory. In this article this is specialized to mean refining the excess formula, which measures the failure of base change, to the level of Deligne's virtual category. We give a natural set of properties for such a refinement, and prove that there exists a unique family of excess formulas on this refined level satisfying these properties.