Duke Mathematical Journal

Hyperbolic Ax–Lindemann theorem in the cocompact case

Emmanuel Ullmo and Andrei Yafaev

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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

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

First available in Project Euclid: 29 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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