Sieving rational points on varieties

Browning, Tim; Loughran, Daniel

doi:10.1090/tran/7514

Sieving rational points on varieties
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by Tim Browning and Daniel Loughran PDF

Trans. Amer. Math. Soc. 371 (2019), 5757-5785 Request permission

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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