Enhanced bivariant homology theory attached to six functor formalism

TL;DR

This paper develops an $ abla$-enhanced bivariant homology theory derived from the six functor formalism, unifying cohomology and Borel-Moore homology within an $ infty$-categorical framework.

Contribution

It introduces an $ abla$-enhanced bivariant homology theory based on Gaitsgory-Rozenblyum's six functor formalism, advancing the categorical understanding of homology theories.

Findings

Constructed an $ abla$-enhanced bivariant homology theory.

Unified cohomology and Borel-Moore homology frameworks.

Extended the six functor formalism to an $ infty$-categorical setting.

Abstract

Bivariant theory is a unified framework for cohomology and Borel-Moore homology theories. In this paper, we extract an $\infty$-enhanced bivariant homology theory from Gaitsgory-Rozenblyum's six functor formalism.