The project gathers specialists of group schemes, Kac-Moody groups, representation theory and automorphic forms, and it adresses arithmetical issues in these fields. One part deals with the theory of group schemes in the spirit of the SGA3 seminar (Demazure- Grothendieck). One other part involves multiple Dirichlet series attached to Kac-Moody root systems of affine type and the last part is about the p-adic Langlands correspondence.