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

Sanghoon Baek

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arXiv · 1502.03023

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

Sanghoon Baek

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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 $n\geq 2$ we completely determine the degree $3$ invariants of a split semisimple group, the quotient of $(\operatorname{\mathbf{SL}}_{2})^{n}$ 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.

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Sanghoon Baek. 2015-02-20. Chow groups of products of Severi-Brauer varieties and invariants of degree 3. https://arxiv.org/abs/1502.03023

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