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Ax-Schanuel for Shimura varieties

Abstract:

We prove the Ax-Schanuel theorem for a general (pure) Shimura variety. A basic version of the theorem concerns the transcendence of the uniformization map from a bounded Hermitian symmetric space to a Shimura variety. We then prove a version of the theorem with derivatives in the setting of jet spaces, and finally a version in the setting of differential fields. Our method of proof builds on previous work, combined with a new approach which uses higher-order contact conditions to place variet...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.4007/annals.2019.189.3.7

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Wolfson College
ORCID:
0000-0003-3958-2338
Tsimerman, J More by this author
Publisher:
Princeton University, Department of Mathematics Publisher's website
Journal:
Annals of Mathematics Journal website
Volume:
189
Issue:
3
Pages:
945-978
Publication date:
2019-05-14
Acceptance date:
2019-02-20
DOI:
ISSN:
1939-8980
Pubs id:
pubs:976078
URN:
uri:629e5fc4-bb28-4cac-aad8-de9994523094
UUID:
uuid:629e5fc4-bb28-4cac-aad8-de9994523094
Local pid:
pubs:976078

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