3 papers
math.NT2023
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…
math.NT2015
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…
math.NT2010
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…