Sieving rational points on varieties

Tim Browning, Daniel Loughran

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)5757-5785
Number of pages29
JournalTransactions of the American Mathematical Society
Volume371
Issue number8
Early online date18 Sep 2018
DOIs
Publication statusE-pub ahead of print - 18 Sep 2018

Cite this

Sieving rational points on varieties. / Browning, Tim; Loughran, Daniel.

In: Transactions of the American Mathematical Society, Vol. 371, No. 8, 18.09.2018, p. 5757-5785.

Research output: Contribution to journalArticle

@article{97ccf88005634f819b5d47f8f96499f4,
title = "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.",
author = "Tim Browning and Daniel Loughran",
year = "2018",
month = "9",
day = "18",
doi = "10.1090/tran/2019-371-08",
language = "English",
volume = "371",
pages = "5757--5785",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "8",

}

TY - JOUR

T1 - Sieving rational points on varieties

AU - Browning, Tim

AU - Loughran, Daniel

PY - 2018/9/18

Y1 - 2018/9/18

N2 - 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.

AB - 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.

U2 - 10.1090/tran/2019-371-08

DO - 10.1090/tran/2019-371-08

M3 - Article

VL - 371

SP - 5757

EP - 5785

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 8

ER -