Applications of the hyperbolic Ax–Schanuel conjecture

C Daw, J Ren - Compositio Mathematica, 2018 - cambridge.org
In 2014, Pila and Tsimerman gave a proof of the Ax–Schanuel conjecture for the-function
and, with Mok, have recently announced a proof of its generalization to any (pure) Shimura …

Tameness in geometry and arithmetic: beyond o-minimality

G Binyamini, D Novikov - International congress of …, 2023 - content.ems.press
The theory of o-minimal structures provides a powerful framework for the study of
geometrically tame structures. In the past couple of decades a deep link connecting o …

[图书][B] Point-Counting and the Zilber–Pink Conjecture

J Pila - 2022 - books.google.com
Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …

Bi-algebraic geometry and the André-Oort conjecture

B Klingler, E Ullmo, A Yafaev - Algebraic geometry: Salt Lake …, 2018 - books.google.com
Shimura varieties are algebraic varieties of enormous interest. Introduced by Shimura and
Deligne in order to generalize the modular curves, they play nowadays a central role in the …

The Ax–Schanuel conjecture for variations of mixed Hodge structures

Z Gao, B Klingler - Mathematische Annalen, 2024 - Springer
The Ax–Schanuel conjecture for variations of mixed Hodge structures | Mathematische
Annalen Skip to main content SpringerLink Account Menu Find a journal Publish with us Track …

Lower bounds for Galois orbits of special points on Shimura varieties: a point-counting approach

G Binyamini, H Schmidt, A Yafaev - Mathematische Annalen, 2023 - Springer
Let S be a Shimura variety. We conjecture that the heights of special points in S (Q¯) are
discriminant negligible with respect to some Weil height function h: S (Q¯)→ R. Assuming …

Structures spéciales et probleme de Zilber-Pink

E Ullmo - Around the Zilber-Pink conjecture/Autour de la …, 2017 - smf.emath.fr
André-Oort conjectures as well as the one formulated by Zilber and Pink concern algebraic
varieties (algebraic tori, Abelian or semi-Abelian varieties, pure or mixed Shimura varieties) …

Heights of pre-special points of Shimura varieties

C Daw, M Orr - Mathematische Annalen, 2016 - Springer
Let s be a special point on a Shimura variety, and xa pre-image of s in a fixed fundamental
set of the associated Hermitian symmetric domain. We prove that the height of x is …

[PDF][PDF] O-minimality as an approach to the André-Oort conjecture

T Scanlon - Panoramas et Synthèses, to appear, 2017 - math.uchicago.edu
Employing a proof technique suggested by Zannier and first successfully implemented by
Pila and Zannier to give a reproof of the Manin-Mumford conjecture on algebraic relations …

Heights of Special Points on Quaternionic Shimura Varieties

R Zhao - arXiv preprint arXiv:2309.08886, 2023 - arxiv.org
Let $ B/F $ be a quaternion algebra over a totally real number field. We give an explicit
formula for heights of special points on the quaternionic Shimura variety associated with $ B …