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Sieving rational points on varieties

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 18 Sep 2018Embargo end date: 01 Jan 2017 United Kingdom English Publisher:American Mathematical Society (AMS)Journal:Transactions of the American Mathematical Society, volume 371, pages 5,757-5,785 (issn: 0002-9947, eissn: 1088-6850, Copyright policy )Funded by:UKRI | Between rational and inte..., NSF | Mathematical Sciences Res...
Authors: Browning, Tim; Loughran, Daniel;

doi: 10.1090/tran/7514 , 10.48550/arxiv.1705.01999

arXiv: 1705.01999

handle: 1983/0a648621-b9c1-40fb-9140-d7ae77075587

Sieving rational points on varieties

Abstract

An upper bound sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, to local solubility in families, and to the notion of “friable” rational points with respect to divisors. In the special case of quadrics, sharper estimates are obtained by developing a version of the Selberg sieve for rational points.

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Keywords

330, quadric, Mathematics - Number Theory, friable, sieve, thin set, 14D10, 510, Applications of the Hardy-Littlewood method, rational points, 11N36, math.NT, varieties, 14G05, 11N36, 11P55, 14D10, Selberg sieve, FOS: Mathematics, Applications of sieve methods, 14G05, Rational points, Number Theory (math.NT), Varieties over global fields, 11P55

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    popularity
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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Top 10%
Top 10%
Top 10%
Green
hybrid