Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Monday, 22 November 2004, 16:00 - 17:00, room 403

Elena Mantovan: The role of the geometry of Shimura varieties in the Langlands program

Abstract:

In a letter to Andreé Weil in 1967, Langlands suggested the existence of a relation between two seemingly unrelated mathematical objects: Galois representations and automorphic representations. Since then, the work of many mathematicians focused on isolating and constructing algebraic varieties whose geometry is supposed to explain the existence of such correspondences. For correspondences defined over a number field, this role is played by Shimura varieties. In my talk I will discuss some aspects of the geometry of the Shimura varieties and how they reflects Langlands' conjectures.