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Congruences for rational points on varieties over finite fields

N. Fakhruddin·C. S. Rajan
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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.

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N. Fakhruddin, C. S. Rajan. 2004-07-07. Congruences for rational points on varieties over finite fields. https://arxiv.org/abs/math/0402230

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