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

By R. Garibaldi. 2000

71 citations recorded by the source corpus.

Abstract. 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f3fdfb18d453da88325f546b41abde8f94a6619