sanghoonbaek@kaist.ac.kr

Submission: 2015, Apr 4

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.

2010 Mathematics Subject Classification: 14M17, 11E72, 14F43, 16H05, 14C25

Keywords and Phrases: Cohomological invariants, Galois cohomology, Chow group, Grothendieck group, torsor, Severiâ€“Brauer varieties, central simple algebras

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