Codimension 2 cycles on products of projective homogeneous surfaces

TL;DR

This paper establishes bounds on torsion in codimension 2 Chow groups for products of projective homogeneous surfaces, including specific cases like Pfister quadrics and Severi-Brauer surfaces, advancing understanding of algebraic cycles.

Contribution

It provides new bounds and exact torsion calculations for products of certain projective homogeneous surfaces, a significant step in algebraic cycle theory.

Findings

Torsion bounds for products of four Pfister quadrics

Maximal torsion for three Severi-Brauer surfaces

Upper bounds for products of three quadrics with same discriminant

Abstract

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