Arithmetic curves lying in compact subsets of affine schemes

Abstract: We will describe the notion of affine schemes and their modifications in the context of Arakelov geometry. Using geometry of numbers in infinite rank, we will study their cohomological properties. Concretely, given an affine scheme X over Z and a compact subset K of the set of complex points of X, we will investigate the geometry of those proper arithmetic curves in X whose complex points lie in K. This is joint work with Jean-Benoît Bost.

number theory

Audience: researchers in the topic

Harvard number theory seminar