Shane Cernele

Abstract: We define and discuss representable functors and groups schemes, as a first step towards describing the various group schemes associated to central simple algebras with involution.

Let p be a prime, r >= 3, and n_i = p^{a_i} for positive integers a_1,...,a_r. Set G = GL_{n_1} x ... x GL_{n_r}, and let \mu be a central subgroup of G. The Galois cohomology set H^1(K, G/\mu) classifies r-tuples of central simple algebras...