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

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.

Rost invariant, cohomological invariant, cup product, Tits class
Mathematical Subject Classification 2010
Primary: 20G15
Secondary: 11E72
Received: 26 September 2016
Revised: 8 February 2017
Accepted: 14 February 2017
Published: 14 September 2017
Skip Garibaldi
IDA Center for Communications Research
San Diego, CA 92121
United States
Alexander S. Merkurjev
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA 90095-1555
United States