An AxSchanuel theorem for the modular curve and the jfunction
Model Theory in Geometry and Arithmetic May 12, 2014  May 16, 2014
Location: SLMath: Eisenbud Auditorium
v1345
The classical AxSchanuel theorem states that, in a differential field, any algebraic relations involving the exponential function must arise in a 'trivial'
manner. It turns out that one can formulate natural analogues of this theorem in the context of uniformization maps arising from Shimura varieties, the simplest case of which is the jfunction. Besides their inherent appeal, such analogues have applications to the ZilberPink conjecture in number theory; a far reaching generalization of AndreOort.
We will explain these analogues and sketch a proof in the case of the jfunction. This is joint work with J.Pila.
v1345
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