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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 anddimension at least f(d), the set X(K) is non-empty. This is a special case of amore general result about intersections of hypersurfaces of fixed degree inprojective spaces of sufficiently high dimension over fields with finitelygenerated Galois groups.

A Weak Chevalley-Warning Theorem for Quasi-finite Fields