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ON THE NUMBER OF POINTS OF SOME VARIETIES OVER FINITE FIELDS

Published online by Cambridge University Press:  12 May 2003

MARC PERRET
MARC PERRET
Affiliation:
Unité de Mathématiques Pures et Appliquées, UMR 5669, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69 363 Lyon Cedex 7, [email protected] GRIMM, Université de Toulouse II le Mirail, 5 Allées Antonio Machado, 31058, Toulouse Cedex, [email protected]
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Abstract

It is proved that the number of ${\bb F}_q$-rational points of an irreducible projective smooth 3-dimensional geometrically unirational variety defined over the finite field ${\bb F}_q$ with $q$ elements is congruent to 1 modulo $q$. Some Fermat 3-folds, some classes of rationally connected 3-folds and some weighted projective $d$-folds also having this property are given.

Keywords

14G1514J3014G05.
Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 3 , May 2003 , pp. 309 - 320
Copyright
© The London Mathematical Society 2003

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