Série de Courts Exposés
# Ax-Lindemann: a statement of functional algebraic independence and bi-algebraicity

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Amphitéâtre Léon Motchane (IHES)
### Amphitéâtre Léon Motchane

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

The Ax-Lindemann(-Weierstrass) theorem is a functional algebraic independence statement for the uniformizing map of an arithmetic variety. For algebraic torus over C this is the analogue of the classical Lindemann-Weierstrass theorem about transcendental numbers to the functional case. This theorem is a key step to prove the André-Oort/Manin-Mumford conjecture by the method of Pila-Zannier. In this talk I will briefly introduce the history of the theorem, explain how to view it as a bi-algebraicity statement and (if time permits) discuss its relationship with the André-Oort/Manin-Mumford conjecture (the latter one known as Raynaud's Theoerem).

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