Linear projections and successive minima

In arithmetic geometry, cohomology groups are not vector spaces as in classical algebraic geometry but rather euclidean lattices. As a consequence, to understand these groups we need to evaluate not only their rank, but also their successive minima, which are fundamental invariants in the geometry of numbers. The goal of this article is to perform this task for line bundles on projective curves. Let K be a number field, OK its ring of integers and E a projective OKmodule of finite rank N . We endow E ⊗ Z C with an hermitian metric h and