Rost invariant of the center, revisited

Skip Garibaldi and Alexander S. Merkurjev

Vol. 291 (2017), No. 2, 369–397

DOI: 10.2140/pjm.2017.291.369

Abstract

The Rost invariant of the Galois cohomology of a simple simply connected algebraic group over a field $F$ is defined regardless of the characteristic of $F$, but certain formulas for it have only been known under a hypothesis on the characteristic. We improve on those formulas by removing the hypothesis on the characteristic and removing an ad hoc pairing that appeared in those formulas. As a preliminary step of independent interest, we also extend the classification of invariants of quasitrivial tori to all fields.

Keywords

Rost invariant, cohomological invariant, cup product, Tits class

Mathematical Subject Classification 2010

Primary: 20G15

Secondary: 11E72

Milestones

Received: 26 September 2016

Revised: 8 February 2017

Accepted: 14 February 2017

Published: 14 September 2017