Bivariant derived algebraic cobordism

TL;DR

This paper develops a new bivariant derived algebraic cobordism theory extending previous work, establishing its properties, and connecting it to algebraic K-theory and Chow rings for singular schemes.

Contribution

It introduces a bivariant derived algebraic cobordism theory, generalizing existing theories and providing new tools for studying singular schemes.

Findings

Defines a bivariant derived algebraic cobordism theory.

Shows the theory specializes to algebraic K^0.

Proposes a candidate for Chow rings of singular schemes.

Abstract

We extend the derived Algebraic bordism of Lowrey and Sch\"urg to a bivariant theory in the sense of Fulton and MacPherson, and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings of singular quasi-projective schemes. The extended cobordism is shown to specialize to algebraic $K^0$ analogously to Conner-Floyd theorem in topology. We also give a candidate for the correct definition of Chow rings of singular schemes.