Congruences for rational points on varieties over finite fields
Number Theory
2007-05-23 v5 Algebraic Geometry
Abstract
We show that the number of rational points on the fibres of a proper morphism of smooth varieties over a finite field k whose generic fibre has a ``trival'' Chow group of zero cycles is congruent to 1 mod |k|. As a consequence we prove that there is a rational point on any degeneration of a smooth proper rationally chain connected variety over a finite field. We also obtain a generalisation of the Chevalley-Warning theorem.
Cite
@article{arxiv.math/0402230,
title = {Congruences for rational points on varieties over finite fields},
author = {N. Fakhruddin and C. S. Rajan},
journal= {arXiv preprint arXiv:math/0402230},
year = {2007}
}
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