9 citations · 41 across the 10 of their papers we have counts for
12 papers
Evaluating the wild Brauer group
Martin Bright, Rachel Newton
Classifying elements of the Brauer group of a variety X over a p-adic field according to the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filt…
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.
Finiteness theorems for K3 surfaces over arbitrary fields
Martin Bright, Adam Logan, Ronald van Luijk
Over an algebraically closed field, various finiteness results are known regarding the automorphism group of a K3 surface and the action of the automorphisms on the Picard lattice.…
Rational points in families of varieties
Martin Bright
Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universität Mainz in October 2017.
Failure of strong approximation on an affine cone
Martin Bright, Ivo Kok
We use the Brauer-Manin obstruction to strong approximation on a punctured affine cone to explain a curious property of coprime integer solutions to a homogeneous Diophantine equat…
A uniform bound on the Brauer groups of certain log K3 surfaces
Martin Bright, Julian Lyczak
Let U be the complement of a smooth anticanonical divisor in a del Pezzo surface of degree at most 7 over a number field k. We show that there is an effective uniform bound for the…
Obstructions to the Hasse principle in families
Martin Bright
For a family of varieties over a number field, we give conditions under which 100% of members have no Brauer-Manin obstruction to the Hasse principle.
Bad reduction of the Brauer-Manin obstruction
Martin Bright
We relate the Brauer group of a smooth variety over a p-adic field to the geometry of the special fibre of a regular model, using the purity theorem in étale cohomology. As an illu…
Brauer groups of singular del Pezzo surfaces
Martin Bright
We describe the effect of rational singularities on the Brauer group of a surface, and compute the Brauer groups of all singular del Pezzo surfaces over an algebraically closed fie…
The Brauer-Manin obstruction on a general diagonal quartic surface
Martin Bright
We prove that, on a sufficiently general diagonal quartic surface, there is a non-trivial Brauer group but no Brauer-Manin obstruction to the existence of rational points.
Torsors under tori and Néron models
Martin Bright
Let R be a Henselian discrete valuation ring with field of fractions K. If X is a smooth variety over K and G a torus over K, then we consider X-torsors under G. If XX/R is a model…
Evaluating Azumaya algebras on cubic surfaces
Martin Bright
Let X be a cubic surface over a local number field k. Given an Azumaya algebra on X, we describe the local evaluation map X(k) -> Q/Z in two cases, showing a sharp dependence on th…