Quelques bords irrationnels de varietes de Shimura

Abstract

We are looking for a formulation of Manin's real multiplication question in higher rank. This question comports, in our point of view, at least two steps: 1. a formalisation of the linear algebra side of the story in terms of morphisms of algebraic groups analogous to Shimura and Deligne's point of view of the theory of complex multiplication. 2. a work of noncommutative algebraic geometry. We are interested only by the first step, and recall the known results in the litterature on the second one. Our point of view, perhaps too naive, is that before looking for a good notion of noncommutative abelian varieties, we have to know what are their periods and what we want to do with them.