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arXiv · 1705.01999

Sieving rational points on varieties

Tim Browning·Daniel Loughran
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Abstract

A sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, the number of varieties in a family which are everywhere locally soluble, 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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Tim Browning, Daniel Loughran. 2017-05-04. Sieving rational points on varieties. https://arxiv.org/abs/1705.01999

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