  In modern form, Hilbert's Theorem 90 tells us that R^1f_*(G_m)=0, where f is
the canonical map between the etale site and the Zariski site of a scheme X. I
construct examples showing that the corresponding statement for algebraic
spaces does not hold. The first example is a nonseparated smooth 1-dimensional
bug-eyed cover in Kollar's sense. The second example is a nonnormal proper
algebraic space obtained by identifying points on suitable nonprojective smooth
proper schemes.
