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

Baek, Sanghoon

doi:10.1090/tran/6772

Chow groups of products of Severi-Brauer varieties and invariants of degree $3$
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Trans. Amer. Math. Soc. 369 (2017), 1757-1771 Request permission

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 $(\mathbf {SL}_{2})^{n}$ 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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