Twisted forms of classical groups

A uniform description is given for the twisted forms of classical reductive group schemes. Such group schemes can be constructed via finite-dimensional algebraic objects, except in the cases of small rank. These objects, augmented odd form algebras, consist of nilpotent groups of class 2 with the action of the ground commutative ring, so we develop a theory of plane descent for them. In addition, classical isotropic reductive groups are described in terms of odd unitary groups up to isogeny.