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14g05.

Bulletin of the London Mathematical Society (1)

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ON THE NUMBER OF POINTS OF SOME VARIETIES OVER FINITE FIELDS
MARC PERRET
Journal:

Bulletin of the London Mathematical Society / Volume 35 / Issue 3 / May 2003

Published online by Cambridge University Press:

12 May 2003, pp. 309-320

Print publication:

May 2003
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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.