What is the earliest possible reference for definition and basic properties of Clifford algebras associated to quadratic modules over a ringed space? The ringed space does not need to be locally ringed, but I am willing to assume that $2$ is invertible in the sheaf of rings if that helps. Searching mathematical reviews revealed a somewhat related paper:

- B. Auslander. The Brauer group of a ringed space. J. Alg. 4 (1966), 220-273.

This paper develops some of the relevant math, but does not talk about the Clifford algebra. I would expect that there is some paper from around the same period defining the Clifford algebra for quadratic modules over a ringed space, but I could not find anything.

I would also be interested if there are papers writing down the Clifford invariant mapping from the Witt group to the Brauer group in the general setting of ringed spaces.

earliest possiblereference. Is there any? (This is a serious question, I'd really like to see a reasonable construction. The scheme-version doesn't generalise immediately, I believe.) $\endgroup$ – Ben Aug 29 '14 at 6:17