Cycle modules and the intersection A-infinity algebra

TL;DR

This paper demonstrates that cycle modules with ring structures induce A-infinity algebra structures on cycle complexes, providing a homotopy model for classical intersection theory in algebraic geometry.

Contribution

It introduces an A-infinity algebra structure on cycle complexes with coefficients in a cycle module, extending intersection theory models.

Findings

Cycle modules with ring structures induce A-infinity algebra structures.

Homotopy models for classical intersection theory are established.

Application to Milnor K-theory connects to algebraic cycle intersection theory.

Abstract

Given a cycle module M with a ring structure we show that the cycle complex with coefficients in M of a smooth scheme of finite type over a field has a A-infinity algebra structure. In the case of Milnor K-theory this gives a homotopy model for the classical intersection theory of algebraic cycles.