On a theorem of Ax

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On the present state of the Andersen-Lempert theory (2010, background): “into itself, which is an embedding outside of codimension (at least) 2 subvariety, is automatically an automorphism [55].”
Tight Bounds For Chevalley–Warning–Ax–Katz Type Estimates, with Improved Applications (2004, methodology): “Katz [7] improved this theorem by showing that the number of zeros is divisible by q , where 1⁄4 m Pr i1⁄41 di max16 i6 rfdegðFiÞg : The results of both Ax and of Katz were obtained by 7rst estimating the divisibility of exponential sums associated to the polynomials.”
Varieties over a finite field with trivial Chow group of 0-cycles have a rational point (2002, methodology): “Again, hypersurfaces of very low degree fulfill the correct congruence ([14]), but I do not know whether it is reflected by this strong Chow group property.”