Vol. 291, No. 2, 2017

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Rost invariant of the center, revisited

Skip Garibaldi and Alexander S. Merkurjev

Vol. 291 (2017), No. 2, 369–397
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
Primary: 20G15
Secondary: 11E72