A Note on Nullstellensatz over Finite Fields

Abstract

We give an expository account of Nullstellensatz-like results when the base field is finite. In particular, we discuss the vanishing ideal of the affine space and of the projective space over a finite field. As an application, we include an alternative proof of Ore's inequality for the number of points of affine hypersurfaces over finite fields.

arXiv comment9 pages; an expository article with minor typos corrected