4 papers · 1 filter
The Hasse norm principle for abelian extensions -- corrigendum
Christopher Frei, Daniel Loughran, Rachel Newton
The proofs of Theorem 1.1 and Theorem 1.5(2) in the authors' paper 'The Hasse norm principle for abelian extensions' are incorrect. We point out the mistakes and provide correct pr…
Normal distribution of bad reduction
Robert J. Lemke Oliver, Daniel Loughran, Ari Shnidman
We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, of curves in these…
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…
Manin's Conjecture for a Singular Sextic del Pezzo Surface
Daniel Loughran
We prove Manin's conjecture for a del Pezzo surface of degree six which has one singularity of type . Moreover, we achieve a meromorphic continuation and explicit exp…