Spinor groups with good reduction.

Let K be a two-dimensional global field of characteristic ≠ 2 and let V be a divisorial set of places of K. We show that for a given n ≥ 5, the set of K-isomorphism classes of spinor groups G = Spinn(q) of nondegenerate n-dimensional quadratic forms over K that have good reduction at all v ∈ V is finite. This result yields some other finiteness properties, such as the finiteness of the genus genK(G) and the properness of the global-to-local map in Galois cohomology. The proof relies on the finiteness of the unramified cohomology groups Hi(K,μ2)V for i ≥ 1 established in the paper. The results for spinor groups are then extended to some unitary groups and to groups of type G2. [ABSTRACT FROM AUTHOR]