Abstract:
The study of Azumaya algebras over schemes has had a
comparatively formidable reputation in algebraic geometry over the past
decades. In this thesis, we provide in the sheaf-theoretic setting
counterparts of results pertaining to involutions of the first kind on
algebras of endomorphisms of faithfully projective -modules, where is a
commutative ring. More precisely, let be a locally finitely presented
module over an affine scheme X, and let be an involution of the first kind
on . Then, there exists an invertible module over the ringed space
such that .
Moreover, given a vector sheaf of finite rank on a locally ringed
space and involution of the first kind on and an invertible -module
such that , then σ locally will depend on an invertible section of .
