Equivariant cobordism of schemes

TL;DR

This paper explores the equivariant cobordism theory of schemes under linear algebraic group actions, comparing it with torus actions and examining implications for the cycle class map of algebraic group classifying spaces.

Contribution

It introduces a comparison between equivariant cobordism theories for different algebraic group actions and analyzes consequences for classifying space cycle maps.

Findings

Comparison of equivariant cobordism for linear algebraic groups and tori

Implications for the cycle class map of algebraic group classifying spaces

New insights into the structure of equivariant cobordism theories

Abstract

We study the equivariant cobordism theory of schemes for action of linear algebraic groups. We compare the equivariant cobordism theory for the action of a linear algebraic groups with similar groups for the action of tori and deduce some consequences for the cycle class map of the classifying space of an algebraic groups.