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arXiv · 1007.3482

The gamma-filtration and the Rost invariant

Skip Garibaldi·Kirill Zainoulline
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Abstract

Let X be the variety of Borel subgroups of a simple and strongly inner linear algebraic group G over a field k. We prove that the torsion part of the second quotient of Grothendieck's gamma-filtration on X is a cyclic group of order the Dynkin index of G. As a byproduct of the proof we obtain an explicit cycle that generates this cyclic group; we provide an upper bound for the torsion of the Chow group of codimension-3 cycles on X; we relate the generating cycle with the Rost invariant and the torsion of the respective generalized Rost motives; we use this cycle to obtain a uniform lower bound for the essential dimension of (almost) all simple linear algebraic groups.

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Skip Garibaldi, Kirill Zainoulline. 2010-07-20. The gamma-filtration and the Rost invariant. https://doi.org/10.1515/crelle-2012-0114

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