Generalizing a theorem of Richard Brauer

There exists a function f : N -> N such that for every positive integer d, every quasi-finite field K and every projective hypersurface X of degree d and dimension >= f (d), the set X (K) is non-empty. This is a special case of a more general result about intersections of hypersurfaces of fixed degree in projective spaces of sufficiently high dimension over fields with finitely generated Galois groups. (c) 2008 Elsevier Inc. All rights reserved.