Cup products, the Heisenberg group, and codimension two algebraic cycles

TL;DR

This paper introduces higher categorical invariants called gerbes for codimension two algebraic cycles, offering a new categorical perspective on divisor intersections and generalizing classical relations in algebraic geometry.

Contribution

It provides a categorical interpretation of divisor intersections using gerbes, extending classical divisor-line bundle relations to higher codimension cycles.

Findings

Defined higher categorical invariants (gerbes) for codimension two cycles

Provided a categorical interpretation of divisor intersections

Generalized the Bloch-Quillen formula

Abstract

We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This generalization of the classical relation between divisors and line bundles furnishes a new perspective on the Bloch-Quillen formula.