[1] Liberté et accumulation, Documenta Math. 22 (2017), 1615—1659
Article
Arxiv
pdf
The principle of Batyrev and Manin and its variants gives a
precise conjectural interpretation for the dominant term
for the number of points of bounded height on an algebraic variety
for which the opposite of the canonical line bundle is sufficiently positive.
As was clearly shown by the counter-example of Batyrev and Tschinkel,
the implementation of this principle requires the exclusion of accumulating
domains which, up to now, are found using an induction procedure on the
dimension of the variety. However this method does not yield a direct
characterisation of the points to be excluded. The aim of this paper is to
propose a measure of freedom for rational points so that the points with
sufficiently positive freedon are randomly distributed on the variety according
to a probability measure on the adelic space introduced by the author in
a previous paper. From that point of view the rational points which
are sufficiently free ought be the ones which respect the principle of Batyrev
and Manin.
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