Série de Courts Exposés

Ax-Lindemann: a statement of functional algebraic independence and bi-algebraicity

by Prof. Ziyang GAO (Université Paris-Sud & IHÉS)

Amphitéâtre Léon Motchane (IHES)

Amphitéâtre Léon Motchane


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