Codimension 2 cycles on Severi-Brauer varieties, by Nikita A. Karpenko

For a given sequence of integers n_i (i runs from 1 to the infinity) we consider all the central simple algebras $A$ (over all fields) satisfying the condition "index of the i-th tensor power of A equals n_i" and find among them an algebra having the biggest torsion in the second Chow group CH^2 of the corresponding Severi-Brauer variety ("biggest" means that it can be mapped epimorphically onto each other). We describe this biggest torsion in a way in general and more explicitly in some important special situations. As an appli- cation we prove indecomposability of certain algebras.

This is a revised version of the same paper.

This paper has appeared in K-Theory 13 (1998), 305-330.

Nikita A. Karpenko <>