Apparaît dans la collection : 2019 - T2 - WS2 - Rational points on irrational varieties

We will explain how studying arithmetic versions of affine schemes and their bira- tional modifications leads to a generalization to arbitrary schemes of both Fekete’s theorem on algebraic integers, all of whose conjugates lie in a certain compact subset of C, and of classical results on approximation of holomorphic functions by polynomials with integral coefficients. We will try and introduce the relevant geom- etry of numbers in infinite rank as a means of studying the cohomology of coherents sheaves on these objects. This is joint work with Jean-Benoît Bost.