Failures of weak approximation in families Page 1 Failures of weak approximation in
families MJ Bright, TD Browning and D. Loughran Compositio Math. 152 (2016), 1435–1475 …

We initiate a systematic quantitative study of subsets of rational points that are integral with
respect to a weighted boundary divisor on Fano orbifolds. We call the points in these sets …

We introduce a general framework for studying special subsets of rational points on an
algebraic variety, termed $\mathcal {M} $-points. The notion of $\mathcal {M} $-points …

We develop a very general version of the hyperbola method which extends the known
method by Blomer and Br\" udern for products of projective spaces to a very large class of …

A conjecture of Manin predicts the asymptotic distribution of rational points of bounded
height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds …

In this article, we apply counting formulas for the number of morphisms from a curve to a toric
variety to three different though related contexts (the first two are to be understood over …

We give a definition of Cox rings and Cox sheaves for varieties over nonclosed fields that is
compatible with torsors under quasitori, including universal torsors. We study their existence …

Given an extension of number fields E⊂ F and a projective variety X over F, we compare the
problem of counting the number of rational points of bounded height on X with that of its Weil …

In order to study integral points of bounded log-anticanonical height on weak del Pezzo
surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a …

Consider a system of polynomials in many variables over the ring of integers of a number
field. We prove an asymptotic formula for the number of integral zeros of this system in …