Codimension 2 cycles on Severi-Brauer varieties

For a given sequence of integers (n(i))(i=1)(infinity) we consider all the central simple algebras A (over all fields) satisfying the condition ind A(xi) = n(i) and find among them an algebra having the biggest torsion in the second Chow group CH2 of the corresponding Severi-Brauer variety ('biggest' means that it can be mapped epimorphically onto each other). We give a description of this biggest torsion in the general case (via the gamma filtration) and find out when (i.e. for which sequences (n(i))(i=1)(infinity)) it is nontrivial. We also make an explicit computation in some special situations, e.g. in the situation of algebras of a square-free exponent e the biggest torsion turns out to be (cyclic) of order e. As an application we prove indecomposability for certain algebras of a prime exponent.