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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2004
 DOI:
 10.48550/arXiv.math/0410269
 arXiv:
 arXiv:math/0410269
 Bibcode:
 2004math.....10269P
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 Mathematics  Quantum Algebra;
 14K10;
 81R60;
 14A22;
 58B34;
 32G05;
 14G35;
 11G18
 EPrint:
 Pages 112. Universitaetsverlag Goettingen, Mathematisches Institut, Seminars. Second of a series of two papers, see math.AG/0410254