Intersection theory in algebraic cobordism

TL;DR

This paper refines the intersection operation in algebraic cobordism, providing a new proof of its functoriality for certain morphisms, enhancing the theoretical framework of algebraic cobordism.

Contribution

It offers a more detailed construction of intersection with pseudo-divisors and a new proof of functoriality in algebraic cobordism.

Findings

Enhanced understanding of intersection operations in algebraic cobordism

New proof of contravariant functoriality for l.c.i. morphisms

Strengthened theoretical foundations of algebraic cobordism

Abstract

We give a more detailed construction of the operation "intersection with a pseudo-divisor" in algebraic cobordism. Using arguments from Levine-Morel, Algebraic Cobordism, sections 6.2, 6.3, this gives a new proof of the contravariant functoriality of algebraic cobordism for l.c.i. morphisms of schemes of finite type over a field of characteristic zero.