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

Ettore Aldrovandi, Niranjan Ramachandran

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.