SIEVING RATIONAL POINTS ON VARIETIES

Tim  Browning; Daniel Loughran

doi:10.1090/tran/7514

SIEVING RATIONAL POINTS ON VARIETIES

Tim Browning, Daniel Loughran

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Abstract

An upper bound sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, 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 language	English
Journal	Transactions of the American Mathematical Society
Early online date	18 Sept 2018
DOIs	https://doi.org/10.1090/tran/7514
Publication status	Published - 2018

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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, 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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year = "2018",

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AB - An upper bound sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, 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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M3 - Article

SN - 0002-9947

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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SIEVING RATIONAL POINTS ON VARIETIES

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