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Counting Rational Points on Cubic Hypersurfaces
Author(s) -
Browning T. D.
Publication year - 2007
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000243
Subject(s) - mathematics , hypersurface , locus (genetics) , cubic form , cubic surface , dimension (graph theory) , pure mathematics , combinatorics , mathematical analysis , cubic function , biochemistry , chemistry , gene
Let X ⊂ ℙ N be a geometrically integral cubic hypersurface defined over ℚ, with singular locus of dimension at most dim X − 4. The main result in this paper is a proof of the fact that X (ℚ) contains O ɛ X ( B dim X + ɛ ) points of height at most B .
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