A Weak Chevalley-Warning Theorem for Quasi-finite Fields
Number Theory
2008-02-27 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0802.3809,
title = {A Weak Chevalley-Warning Theorem for Quasi-finite Fields},
author = {Michael Larsen and Bo-Hae Im},
journal= {arXiv preprint arXiv:0802.3809},
year = {2008}
}
Comments
Introduction now acknowledges a paper of Ax