25 citations · 111 across the 35 of their papers we have counts for
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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…
An effective Arakelov-theoretic version of the hyperbolic isogeny theorem
Ariyan Javanpeykar
For an integer and hyperbolic curve over , Mochizuki showed that there are only finitely many isomorphism classes of hyperbolic curves of Euler ch…
The moduli of smooth hypersurfaces with level structure
Ariyan Javanpeykar, Daniel Loughran
We construct the moduli space of smooth hypersurfaces with level structure over . As an application we show that, for large enough, the stack of smooth hyp…
Complete intersections: Moduli, Torelli, and good reduction
Ariyan Javanpeykar, Daniel Loughran
We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conje…
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…