Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T22:01:13.921Z Has data issue: false hasContentIssue false
  • English
  • Français

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, Franceperret@umpa.ens-lyon.fr GRIMM, Université de Toulouse II le Mirail, 5 Allées Antonio Machado, 31058, Toulouse Cedex, Franceperret@univ-tlse2.fr
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)