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IX - Group schemes

Published online by Cambridge University Press:  07 November 2024

Skip Garibaldi ,
Holger P. Petersson  and
Michel L. Racine
Skip Garibaldi
Affiliation:
Institute for Defense Analyses, USA
Holger P. Petersson
Affiliation:
FernUniversität in Hagen
Michel L. Racine
Affiliation:
University of Ottawa
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Summary

In most of this book, we have studied Albert and octonion algebras. In this chapter, we connect those with the theory of semi-simple affine group schemes, especially those of type E6, F4, and G2. As part of this effort, we give an introduction to non-abelian flat cohomology and its applications to descent. We leverage this together with known results about affine group schemes such as Gross’s mass formula to classify the Albert algebras over the integers, a recently discovered result.

Keywords

Semisimple groupgroup schemeflat cohomologyGalois cohomologyG2F4E6descent theoremAlbert algebras over Ztensor system
Type
Chapter
Information
Albert Algebras over Commutative Rings
The Last Frontier of Jordan Systems
 , pp. 567 - 619
Publisher: Cambridge University Press
Print publication year: 2024

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