17 citations · 64 across the 22 of their papers we have counts for
5 papers · 2 filters
Good reduction of Fano threefolds and sextic surfaces
Ariyan Javanpeykar, Daniel Loughran
We investigate versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings, for other classes of varieties. We first obtain analogues for certain…
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…
The Hasse norm principle for abelian extensions
Christopher Frei, Daniel Loughran, Rachel Newton
We study the distribution of abelian extensions of bounded discriminant of a number field which fail the Hasse norm principle. For example, we classify those finite abelian gro…
The Hasse principle for lines on diagonal surfaces
Jörg Jahnel, Daniel Loughran
Given a number field and a positive integer , in this paper we consider the following question: does there exist a smooth diagonal surface of degree in ov…
Good reduction of algebraic groups and flag varieties
Ariyan Javanpeykar, Daniel Loughran
In 1983, Faltings proved that there are only finitely many abelian varieties over a number field of fixed dimension and with good reduction outside a given set of places. In this p…