Arne Smeets

activity

20122023

most citedCampana points of bounded height on vector group compactifications

13 citations · 39 across the 9 of their papers we have counts for

collaborators

11 papers

math.NT2023★ 2 cited

Paucity of rational points on fibrations with multiple fibres

Tim Browning, Julian Lyczak, Arne Smeets

Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allo…

math.AG2022

On logarithmic reduction of cohomologically tame elliptic surface

Otto Overkamp, Arne Smeets

We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in p…

math.NT2019★ 13 cited

Campana points of bounded height on vector group compactifications

Marta Pieropan, Arne Smeets, Sho Tanimoto +1

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 the…

math.AG2019★ 6 cited

Failure of the Brauer-Manin principle for a simply connected fourfold over a global function field, via orbifold Mordell

Stefan Kebekus, Jorge Vitório Pereira, Arne Smeets

Almost one decade ago, Poonen constructed the first examples of algebraic varieties over global fields for which Skorobogatov's etale Brauer-Manin obstruction does not explain the…

math.AG2017★ 3 cited

Logarithmic good reduction and the index

Kentaro Mitsui, Arne Smeets

Let $K$ be the fraction field of a complete discrete valuation ring, with algebraically closed residue field of characteristic $p > 0$ . This paper studies the index of a smooth, pr…

math.AG2017★ 1 cited

Pseudo-split fibres and arithmetic surjectivity

Daniel Loughran, Alexei N. Skorobogatov, Arne Smeets

Let $f : X \to Y$ be a dominant morphism of smooth, proper and geometrically integral varieties over a number field $k$ , with geometrically integral generic fibre. We give a necessa…

math.AG2015

Logarithmic good reduction of abelian varieties

Alberto Bellardini, Arne Smeets

Let $K$ be a field which is complete for a discrete valuation. We prove a logarithmic version of the Néron-Ogg-Shafarevich criterion: if $A$ is an abelian variety over $K$ which is…

math.NT2015

Fibrations with few rational points

Daniel Loughran, Arne Smeets

We study the problem of counting the number of varieties in families which have a rational point. We give conditions on the singular fibres that force very few of the varieties in…

math.AG2015★ 5 cited

Logarithmic good reduction, monodromy and the rational volume

Arne Smeets

Let $R$ be a strictly local ring complete for a discrete valuation, with fraction field $K$ and residue field of characteristic $p > 0$ . Let $X$ be a smooth, proper variety over $K…

math.NT2014

Insufficiency of the étale Brauer-Manin obstruction: towards a simply connected example

Arne Smeets

Since Poonen's construction of a variety $X$ defined over a number field $k$ for which $X (k)$ is empty and the étale Brauer--Manin set $X (A_{k})^{Br,et}$ is not, severa…

math.NT2012★ 9 cited

Universal torsors and values of quadratic polynomials represented by norms

Ulrich Derenthal, Arne Smeets, Dasheng Wei

Let $K / k$ be an extension of number fields, and let $P (t)$ be a quadratic polynomial over $k$ . Let $X$ be the affine variety defined by $P (t) = N_{K / k} (z)$ . We study the H…