Ax-Lindemann: a statement of functional algebraic independence and bi-algebraicity
(Université Paris-Sud & IHÉS)
Amphitéâtre Léon Motchane (IHES)
Amphitéâtre Léon Motchane
Le Bois Marie
35, route de Chartres
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).