Sanghoon Baek: On the torsion of Chow groups of Severi-Brauer varieties

Submission: 2013, Nov 10

In this paper, we generalize a result of Karpenko on the torsion in the second quotient of the gamma filtration for Severi-Brauer varieties to higher degrees. As an application, we provide a nontrivial torsion in higher Chow groups and the topological filtration of the associated generic variety and obtain new upper bounds for the annihilators of the torsion subgroups in the Chow groups of a large class of Severi-Brauer varieties. In particular, using the torsion in higher degrees, we find new indecomposable algebras.

2010 Mathematics Subject Classification: 14C25, 16H05, 20G15

Keywords and Phrases: Torsion, Severi Brauer varieties, central simple algebra, Chow group, Grothendieck group, topological filtration, gamma filtration

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