Mathematics – Algebraic Geometry
Scientific paper
2010-07-20
Mathematics
Algebraic Geometry
19 pages; this is an essentially extended version of the previous preprint. Applications to cohomological invariants and essen
Scientific paper
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.
Garibaldi Skip
Zainoulline Kirill
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