  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.
