JournalscmhVol. 76, No. 4pp. 684–711

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

  • R. S. Garibaldi

    UCLA, Los Angeles, USA
The Rost invariant has trivial kernel for quasi-split groups of low rank cover
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Abstract

For G a simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map RG:H1(F,G)H3(F,Q/Z(2))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.

Cite this article

R. S. Garibaldi, The Rost invariant has trivial kernel for quasi-split groups of low rank. Comment. Math. Helv. 76 (2001), no. 4, pp. 684–711

DOI 10.1007/S00014-001-8325-8