Ariyan Javanpeykar, Daniel Loughran
Published 2015-05-09Version 1
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 conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.
Cycles in the de Rham cohomology of abelian varieties over number fields
The geometric torsion conjecture for abelian varieties with real multiplication
Infinitely $p$-divisible points on abelian varieties defined over function fields of characteristic $p>0$
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