Duke Mathematical Journal

Hyperbolic Ax–Lindemann theorem in the cocompact case

Emmanuel Ullmo and Andrei Yafaev

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Abstract

We prove an analogue of the classical Ax–Lindemann theorem in the context of compact Shimura varieties. Our work is motivated by Pila’s strategy for proving the André–Oort conjecture unconditionally.

Article information

Source
Duke Math. J., Volume 163, Number 2 (2014), 433-463.

Dates
First available in Project Euclid: 29 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1391007591

Digital Object Identifier
doi:10.1215/00127094-2410546

Mathematical Reviews number (MathSciNet)
MR3161318

Zentralblatt MATH identifier
1375.14096

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18] 53C38: Calibrations and calibrated geometries
Secondary: 11J91: Transcendence theory of other special functions

Citation

Ullmo, Emmanuel; Yafaev, Andrei. Hyperbolic Ax–Lindemann theorem in the cocompact case. Duke Math. J. 163 (2014), no. 2, 433--463. doi:10.1215/00127094-2410546. https://projecteuclid.org/euclid.dmj/1391007591


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