Published online by Cambridge University Press: 07 November 2024
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.
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