Alexander Merkurjev, Alexander Neshitov, Kirill Zainoulline: Invariants of degree 3 and torsion in the Chow group of a versal flag

Submission: 2014, Jan 9

We prove that the group of normalized cohomological invariants of degree 3 modulo the subgroup of semidecomposable invariants of a semisimple split linear algebraic group G is isomorphic to the torsion part of the Chow group of codimension 2 cycles of the respective versal G-flag. In particular, if G is simple, we show that this factor group is isomorphic to the group of indecomposable invariants of G. As an application, we construct nontrivial cohomological classes for indecomposable central simple algebras.

2010 Mathematics Subject Classification: 11E72, 14M17, 14F43

Keywords and Phrases: cohomological invariant, linear algebraic group, torsor, Galois cohomology, Chow group.

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