Clifford algebras of O_X-quadratic spaces

In the classical theory of quadratic forms and Clifford algebras, it is a well-known result that, given a finitely generated projective module P, if H[P] denotes the associated hyperbolic space of P, then the (graded) algebras Cl(H[P]) and End(^(P)) are isomorphic.  We investigate the conditions under which a counterpart of this result holds in the sheaf-theoretic context.  Next, we introduce standard involutions for O_X-algebras associated with K-algebras, where K is a unital commutative ring with no zero-divisors for the purpose of defining graded quadratic extensions of the ringed space (X, O_X), where X = Spec K.

This is joint work with C. Ndipingwi.

Also see the attached file.