Chow groups of products of Severi-Brauer varieties and invariants of degree 3

2015/02/10 by Sanghoon Baek, Baek, Sanghoon
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.AG #math.RA

paper · pdf · doi:10.48550/arxiv.1502.03023

Lemma 7.1 and Prop. 7.3 corrected

arxiv created 2015/02/20 · arxiv updated 2015/02/23

Abstract

We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension 2 Chow groups of a product of Severi-Brauer varieties. In particular, for any n≥ 2 we completely determine the degree 3 invariants of a split semisimple group, the quotient of (SL₂)ⁿ by its maximal central subgroup, as well as of the corresponding split reductive group. We also provide an example illustrating that a modification of our method can be applied to find the semi-decomposable invariants of a split semisimple group of type A.

Related

• On the torsion of Chow groups of Severi-Brauer varieties
• On the Brauer group of the product of a torus and a semisimple algebraic group
• Schubert cycles and subvarieties of generalized Severi-Brauer varieties
• The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves
• Secant varieties and degrees of invariants