Commentarii Mathematici Helvetici


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Volume 76, Issue 4, 2001, pp. 684–711
DOI: 10.1007/s00014-001-8325-8

Published online: 2001-12-31

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

R. S. Garibaldi[1]

(1) UCLA, Los Angeles, USA

For G a simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map $ R_G : H^1(F, G) \rightarrow H^3(F, \mathbb{Q} / \mathbb{Z}(2)) $. This includes the Arason invariant for quadratic forms and Rost's mod 3 invariant for exceptional Jordan algebras as special cases. We show that RG 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.

Keywords: Rost invariant, exceptional groups

Garibaldi R.: The Rost invariant has trivial kernel for quasi-split groups of low rank. Comment. Math. Helv. 76 (2001), 684-711. doi: 10.1007/s00014-001-8325-8