54 citations · 142 across the 14 of their papers we have counts for
7 papers · 1 filter
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…
Campana points, Vojta's conjecture, and level structures on semistable abelian varieties
Dan Abramovich, Anthony Várilly-Alvarado
We introduce a qualitative conjecture, in the spirit of Campana, to the effect that certain subsets of rational points on a variety over a number field, or a Deligne-Mumford stack…
Abelian -division fields of elliptic curves and Brauer groups of product Kummer & abelian surfaces
Anthony Várilly-Alvarado, Bianca Viray
Let be a principal homogeneous space of an abelian surface, or a K3 surface, over a finitely generated extension of . In 2008, Skorobogatov and Zarhin showed that t…
Failure of the Hasse principle for Enriques surfaces
Anthony Várilly-Alvarado, Bianca Viray
We construct an Enriques surface X over Q with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer-Manin obstruction to the Hasse principle…
Density of rational points on isotrivial rational elliptic surfaces
Anthony Várilly-Alvarado
For a large class of isotrivial rational elliptic surfaces (with section), we show that the set of rational points is dense for the Zariski topology, by carefully studying variatio…
Arithmetic E_8 lattices with maximal Galois action
Anthony Várilly-Alvarado, David Zywina
We construct explicit examples of E_8 lattices occurring in arithmetic for which the natural Galois action is equal to the full group of automorphisms of the lattice, i.e., the Wey…
Weak approximation on del Pezzo surfaces of degree 1
Anthony Várilly-Alvarado
We study del Pezzo surfaces of degree 1 of the form w^2 = z^3 + Ax^6 + By^6 in the weighted projective space P_k(1,1,2,3), where k is a perfect field of characteristic not 2 or 3 a…