Rationally trivial hermitian spaces are locally trivial

Abstract.

Let R be a regular local ring, K its field of fractions and A an Azumaya algebra with involution over R. Let h be an $\epsilon$-hermitian space over A. We show that if $\bold{h}\otimes_R K$ is hyperbolic over $A\otimes_R K$, then h is hyperbolic over A.