Yafaev: Galois orbits and equidistribution: Manin-Mumford and André-Oort.

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Andrei Yafaev
Galois orbits and equidistribution: Manin-Mumford and André-Oort.
Journal de théorie des nombres de Bordeaux, 21 no. 2 (2009), p. 491-500, doi: 10.5802/jtnb.684
Article PDF | Reviews MR 2541439 | Zbl 1209.11055

Résumé - Abstract

We overview a unified approach to the André-Oort and Manin-Mumford conjectures based on a combination of Galois-theoretic and ergodic techniques. This paper is based on recent work of Klingler, Ullmo and Yafaev on the André-Oort conjecture, and of Ratazzi and Ullmo on the Manin-Mumford conjecture.

Bibliography

[1] F. Breuer, Special subvarieties of Drinfeld modular varieties. Preprint, 2009. Available on author’s web-page. arXiv
[2] L. Clozel, E. Ullmo, Equidistribution de sous-variétés spéciales. Annals of Mathematics 161 (2005), 1571–1588. MR 2180407 | Zbl 1099.11031
[3] P. Deligne, Variétés de Shimura : interpretation modulaire et techniques de construction de modeles canoniques. In Automorphic Forms, Representations and $L$-functions. Part II, Vol 33 of Proc. of Symp. in Pure Math., 247–290, AMS. MR 546620 | Zbl 0437.14012
[4] B. Klingler, A. Yafaev, The André-Oort conjecture. Preprint, submitted. Available on Klingler’s web-page.
[5] N. Ratazzi, E. Ullmo, Galois+Equidistribution=Manin-Mumford. Preprint. To appear in the Proceedings of Clay summer school on Arithmetic Geometry, Goettingen, 2007. Available on Ullmo’s web-page.
[6] E. Ullmo, A. Yafaev, The André-Oort conjecture for products of modular curves. Preprint. To appear in the Proceedings of Clay summer school on Arithmetic Geometry, Goettingen, 2007. Available on Ullmo’s web-page.
[7] E. Ullmo, A. Yafaev, Galois orbits and equidistribution : towards the André-Oort conjecture. Preprint, submitted. Available on Ullmo’s web-page.
[8] R. Pink, A Combination of the Conjectures of Mordell-Lang and André-Oort. In Geometric Methods in Algebra and Number Theory (Bogomolov, F., Tschinkel, Y., Eds.), Progress in Mathematics 253, Birkhäuser, 2005, 251–282. MR 2166087 | Zbl pre05013101
[9] R. Pink, A Common Generalization of the Conjectures of André-Oort, Manin-Mumford, and Mordell-Lang. Preprint available on author’s web-page.
[10] P. Tzermias, The Manin-Mumford conjecture: a brief survey. Bull. London Math. Soc. 32 (2000), no. 6, 641–652. MR 1781574 | Zbl 1073.14525
[11] A. Yafaev, A conjecture of Yves André’s. Duke Mathematical Journal. 132 (2006), no. 3, 393–407. Article | MR 2219262 | Zbl 1097.11032