A Weak Chevalley-Warning Theorem for Quasi-finite Fields

Details A Weak Chevalley-Warning Theorem for Quasi-finite Fields A Weak Chevalley-Warning Theorem for Quasi-finite Fields

2008-02-26

arxiv.org/abs/0802.3809v2

Mathematics

Number Theory

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Scientific paper

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.

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