On the norm principle for quadratic forms

Abstract

We prove a version of Knebusch's Norm Principle for finite étale extensions of semi-local Noetherian domains with infinite residue fields of characteristic different from 2. As an application we prove Grothendieck's conjecture on principal homogeneous spaces for the spinor group of a quadratic space.

14 pages, hyperref, xypic, (This is an extended and revised version of the previous preprint: The proof of Grothendieck's conjecture on Principal Homogeneous Spaces for the case of spinor group was added)