Forthcoming events in this series


Thu, 04 Mar 2010
14:00
L3

On the field with one element

Pierre Cartier
(IHES)
Abstract

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropial geometry).

Wed, 03 Mar 2010
11:00
L1

On the field with one element

Pierre Cartier
(IHES)
Abstract

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).

Tue, 02 Mar 2010
17:00
L2

On the field with one element

Pierre Cartier
(IHES)
Abstract

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).

Thu, 05 Mar 2009

11:00 - 12:00
L2

Decomposition theorem for abelian fibrations

Professor Bao Chau Ngo
(Orsay)
Abstract

Derived direct image of a proper map with smooth source is a direct sum of simple perverse sheaves with shifts in the degrees. The supports of these simple perverse sheaves are obviously important  topological invariants of the map. In general, it is difficult to determine these supports. This is possible for an abelian fibration under some assumptions. This determination has some amazing  consequences on equality of number of points of certain algebraic varieties over finite fields and in particular, it implies the so called fundamental lemma in Langlands' program.