Sieving rational points on varieties

2017/05/04 by Browning, Tim, Loughran, Daniel · 2 citations
#11N36 #11P55 #14D10 #14G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1705.01999

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.

Cited by

• Hilbert properties of varieties
• An improved large sieve for quadratic characters via Hooley neutralisers and its applications

Related

• The number of varieties in a family which contain a rational point
• The leading constant for rational points in families
• Equidistribution of rational points and the geometric sieve for toric varieties
• Fibrations with few rational points
• Rational points in families of varieties