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arXiv · 1312.0842

Invariants of degree 3 and torsion in the Chow group of a versal flag

Alexander Merkurjev·Alexander Neshitov·Kirill Zainoulline
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Abstract

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.

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Alexander Merkurjev, Alexander Neshitov, Kirill Zainoulline. 2014-10-08. Invariants of degree 3 and torsion in the Chow group of a versal flag. https://doi.org/10.1112/s0010437x14008057

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