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In the present paper, we provide general bounds for the torsion in thecodimension 2 Chow groups of the products of projective homogeneous surfaces.In particular, we determine the torsion for the product of four Pfister quadricsurfaces and the maximal torsion for the product of three Severi-Brauersurfaces. We also find an upper bound for the torsion of the product of threequadric surfaces with the same discriminant.

Codimension 2 cycles on products of projective homogeneous surfaces