Ax-Schanuel results for Shimura varieties
Ax-Schanuel results for Shimura varieties
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Jonathan Pila, University of Oxford
I will describe recent work with Ngaiming Mok and Jacob Tsimerman听giving analogues of ``Ax-Schanuel'' for Shimura varieties. I will sketch听 the role of ``o-minimal structures''in the proof, in particular point counting听and powerful algebraicity results of Peterzil-Starchenko, in combination听with hyperbolic geometry and monodromy, and describe versions in the setting听of a differential field.