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On the Number of Points of Some Varieties Over Finite Fields
Author(s) -
Perret Marc
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001820
Subject(s) - mathematics , fermat's last theorem , modulo , finite field , variety (cybernetics) , projective variety , mathematics subject classification , pure mathematics , rational point , projective test , combinatorics , field (mathematics) , discrete mathematics , mathematical analysis , statistics , algebraic number
It is proved that the number of F q ‐rational points of an irreducible projective smooth 3‐dimensional geometrically unirational variety defined over the finite field 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. 2000 Mathematics Subject Classification 14G15, 14J30, 14G05.