Equivariant Algebraic Cobordism

TL;DR

This paper develops an equivariant algebraic cobordism theory applicable to schemes with linear algebraic group actions over fields of characteristic zero, extending algebraic topology concepts into algebraic geometry.

Contribution

It introduces a new equivariant algebraic cobordism framework for schemes with group actions, expanding the tools available in algebraic geometry.

Findings

Constructed the equivariant algebraic cobordism theory.

Proved foundational properties of the theory.

Demonstrated applications to schemes with group actions.

Abstract

We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.