6 papers
Brauer-Manin obstruction for Erdős-Straus surfaces
Martin Bright, Daniel Loughran
We study the failure of the integral Hasse principle and strong approximation for the Erdős-Straus conjecture using the Brauer-Manin obstruction.
Rank jumps on elliptic surfaces and the Hilbert property
Daniel Loughran, Cecília Salgado
Given an elliptic surface over a number field, we study the collection of fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable assumptions, we show that…
Inverse Galois problem for del Pezzo surfaces over finite fields
Daniel Loughran, Andrey Trepalin
We completely solve the inverse Galois problem for del Pezzo surfaces of degree and over all finite fields.
Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem
Ariyan Javanpeykar, Daniel Loughran
We prove an analogue for algebraic stacks of Hermite-Minkowski's finiteness theorem from algebraic number theory, and establish a Chevalley-Weil type theorem for integral points on…
Sieving rational points on varieties
Tim Browning, Daniel Loughran
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 e…
Counting curve types
Tarik Aougab, Juan Souto
Let be a closed orientable hyperbolic surface, and let denote the number of mapping class group orbits of curves on with at most self-intersections.…