2015/05/09 by Javanpeykar, Ariyan, Loughran, Daniel
#11G35 (Primary) #14C34 #14D23 (Secondary) #14J50 #14K30 #14M10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1505.02249
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.