A Weak Chevalley-Warning Theorem for Quasi-finite Fields
Larsen, Michael, Bo‐Hae Im · arXiv (Cornell University) · 2008
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 at least 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.