A generalization of the Picard-Brauer exact sequence

TL;DR

This paper generalizes the Picard-Brauer exact sequence to higher codimensions, linking Chow groups with a Brauer-like group for smooth varieties, expanding the theoretical framework of algebraic cycles.

Contribution

It extends Lichtenbaum's argument to higher codimensions, resulting in a new exact sequence connecting Chow groups and Brauer-like groups for smooth varieties.

Findings

Generalized the Picard-Brauer exact sequence to higher codimensions

Connected Chow groups with Brauer-like groups in a new exact sequence

Enhanced understanding of algebraic cycles and their cohomological invariants

Abstract

We extend an argument of S.Lichtenbaum involving codimension one cycles to higher codimensions and obtain a generalization of the well-known Picard-Brauer exact sequence for a smooth variety X. The resulting exact sequence connects the codimension n Chow group of X with a certain "Brauer-like" group.