Multiplicative property of localized Chern characters for 2-periodic complexes

TL;DR

This paper proves that localized Chern characters are multiplicative, enabling a ring homomorphism from K-groups of periodic complexes to bivariant Chow cohomology, and demonstrates the functoriality of cosection-localized intersection homomorphisms.

Contribution

It establishes the multiplicative property of localized Chern characters and applies this to prove functoriality of cosection-localized intersection homomorphisms.

Findings

Localized Chern characters are multiplicative.

A ring homomorphism from K-group to bivariant Chow cohomology is constructed.

Functoriality of cosection-localized intersection homomorphisms is proved.

Abstract

We prove the multiplicative property of localized Chern characters. As a direct consequence, a localized Chern character gives rise to a ring homomorphism from the K-group of periodic complexes to the bivariant Chow cohomology group. As an application, we prove the functoriality of Kiem-Li's cosection-localized intersection homomorphisms.