ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification:11E70, 11E81, 12G05, 14F20, 19E15. R. Sujatha, School of Maths, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, INDIA. Unramified cohomology groups of quadrics Given a smooth, proper, integral variety X over a field F of characteristic not 2, let F (X) denote the function field of X. The unramified cohomology groups of X are subgroups of the Galois cohomology groups of F (X) and are birational invariants of X. If X/F is birational to projective space, then these groups coincide with the cohomology groups of F. We present some results obtained in joint work with B. Kahn and M. Rost on the unramified cohomology groups of smooth projective anisotropic quadrics over F (i. e. quadrics which do not have an F -rational point).