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, 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

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