Projectivity in Algebraic Cobordism

TL;DR

This paper shows that in algebraic cobordism over a field of characteristic zero, the assumption that cycles come from quasiprojective varieties can be removed without changing the theory.

Contribution

It proves that the quasiprojectivity condition is unnecessary in defining algebraic cobordism over characteristic zero fields.

Findings

Quasiprojectivity can be omitted in algebraic cobordism over characteristic zero fields.

The algebraic cobordism group remains unchanged without the quasiprojectivity assumption.

The result simplifies the understanding of algebraic cobordism in characteristic zero.

Abstract

The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the same theory.