Hermitian Vector Bundles on Arithmetic Varieties

摘要

We present in these notes a geometric approach to algebraic varieties over Zknown as Arakelov theory because of the fundamental papers by Arakelov in dimension two. Given a regular, projective and flat scheme X over Z, we shall study the hermitian vector bundles over X. By this we mean pairs (E,h) consisting of an algebraic vector bundle Ec on the analytic complex manifold X(c) (h is also required to be invariant under complex conjugation). We shall try to persuade the reader that hermitian vector bundles enjoy properties which are completely parallel to those of algebraic vector bundles on smooth projective complex manifolds.