For any variety X, and for any coefficient ring S, we define the S-topological filtration on the Grothendieck group of coherent sheaves G(X) ⊗ S with coefficients in S. The S-topological filtration is related to the topological filtration by means of a universal coefficient theorem. We apply this observation in the case X is a Severi-Brauer variety to obtain new examples of torsion in the Chow groups of X.

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