• Corpus ID: 116893780

Quelques bords irrationnels de varietes de Shimura

@article{Paugam2004QuelquesBI,
  title={Quelques bords irrationnels de varietes de Shimura},
  author={Fr'ed'eric Paugam},
  journal={arXiv: Algebraic Geometry},
  year={2004}
}
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… 

Three examples of noncommutative boundaries of Shimura varieties

We study the noncommutative modular curve (which was already studied by Connes, Manin and Marcolli), and the space of geodesics on the usual modular curve, from the viewpoint of algebraic groups,

Lectures on Arithmetic Noncommutative Geometry

This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004.

References

SHOWING 1-9 OF 9 REFERENCES

Continued fractions, modular symbols, and noncommutative geometry

Abstract. Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take

Three examples of noncommutative boundaries of Shimura varieties

We study the noncommutative modular curve (which was already studied by Connes, Manin and Marcolli), and the space of geodesics on the usual modular curve, from the viewpoint of algebraic groups,

Noncommutative Geometry and Number Theory

In almost every branch of mathematics we use the ring of rational integers, yet in looking beyond the formal structure of this ring we often encounter great gaps in our understanding. The need to

Compactifications of Locally Symmetric Spaces

Let G be the real locus of a connected semisimple linear algebraic group G defined over Q, and Γ ⊂ G(Q) an arithmetic subgroup. Then the quotient Γ\G is a natural homogeneous space, whose quotient on

Noncommutative differential geometry, Inst

  • Hautes Études Sci. Publ. Math. (1985),
  • 1985

Darmon : autre approche : points de Hegner-Stark sur les courbes elliptiques sur Q conjecturalement définis sur des corps de classe

    Φ(τ ) = (σ · 1) × (τ · 1) = σ · (1 × (τ · 1))) = σ · (τ · 1) = (στ ) · 1

    • Classification of holomorphic vector bundles on noncommutative two-tori, arXiv
    • 2003