Congruences for rational points on varieties over finite fields

Details Congruences for rational points on varieties over finite fields Congruences for rational points on varieties over finite fields

2004-02-13

arxiv.org/abs/math/0402230v5

Mathematics

Number Theory

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Scientific paper

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.

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