The Rost invariant has trivial kernel for quasi-split groups of low rank

2000/09/30 by R. Skip Garibaldi · 1 citation
Mathematics · #math.GR #math.RA #msc:20G10 #msc:17B25

paper · pdf

published as Comment. Math. Helv., vol. 76 (2001) 684-711 · Author-supplied DVI/PS files available at http://www.math.ucla.edu/~skip/preprints.html Minor changes since first edition

arxiv created 2000/10/31 · arxiv updated 2009/11/30

Abstract

For G an almost simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map R_G: H¹(F, G) --> H³(F, Q/Z(2)). This includes the Arason invariant for quadratic forms and Rost's mod 3 invariant for Albert algebras as special cases. We show that R_G has trivial kernel if G is quasi-split of type E₆ or E₇. A case-by-case analysis shows that it has trivial kernel whenever G is quasi-split of low rank.

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