Unramified cohomology of quadrics, II, by B. Kahn and R. Sujatha

We continue our investigation of the unramified cohomology of smooth projective quadrics started in part I. Here we concentrate on quadrics X of dimension 2,3 and 4, and obtain detailed results. In particular, if X is defined by a "virtual Albert form" q, we relate the degree 4 unramified cohomology of X to the group PSO(q)/R, where R denotes Manin's R-equivalence.

Quadrics of dimension > 4 are studied in the forthcoming part III of this series.

B. Kahn <kahn@math.jussieu.fr>
R. Sujatha <sujatha@math.tifr.res.in>