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

Andrei Yafaev[1]

  • [1] University College London Department of Mathematics Gower street, WC1E 6BT, London, United Kingdom

Journal de Théorie des Nombres de Bordeaux (2009)

  • Volume: 21, Issue: 2, page 491-500
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Yafaev, Andrei. "Galois orbits and equidistribution: Manin-Mumford and André-Oort.." Journal de Théorie des Nombres de Bordeaux 21.2 (2009): 491-500. <http://eudml.org/doc/10894>.

@article{Yafaev2009,
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.},
affiliation = {University College London Department of Mathematics Gower street, WC1E 6BT, London, United Kingdom},
author = {Yafaev, Andrei},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Manin-Mumford conjecture; André-Oort conjecture; abelian varieties; Shimura varieties; special points; equidistribution},
language = {eng},
number = {2},
pages = {491-500},
publisher = {Université Bordeaux 1},
title = {Galois orbits and equidistribution: Manin-Mumford and André-Oort.},
url = {http://eudml.org/doc/10894},
volume = {21},
year = {2009},
}

TY - JOUR
AU - Yafaev, Andrei
TI - Galois orbits and equidistribution: Manin-Mumford and André-Oort.
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2009
PB - Université Bordeaux 1
VL - 21
IS - 2
SP - 491
EP - 500
AB - 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.
LA - eng
KW - Manin-Mumford conjecture; André-Oort conjecture; abelian varieties; Shimura varieties; special points; equidistribution
UR - http://eudml.org/doc/10894
ER -

References

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  1. F. Breuer, Special subvarieties of Drinfeld modular varieties. Preprint, 2009. Available on author’s web-page. 
  2. L. Clozel, E. Ullmo, Equidistribution de sous-variétés spéciales. Annals of Mathematics 161 (2005), 1571–1588. Zbl1099.11031MR2180407
  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. Zbl0437.14012MR546620
  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. Zbl1254.11062
  7. E. Ullmo, A. Yafaev, Galois orbits and equidistribution : towards the André-Oort conjecture. Preprint, submitted. Available on Ullmo’s web-page. Zbl1328.11070
  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. Zbl1200.11041MR2166087
  9. R. Pink, A Common Generalization of the Conjectures of André-Oort, Manin-Mumford, and Mordell-Lang. Preprint available on author’s web-page. Zbl1200.11041
  10. P. Tzermias, The Manin-Mumford conjecture: a brief survey. Bull. London Math. Soc. 32 (2000), no. 6, 641–652. Zbl1073.14525MR1781574
  11. A. Yafaev, A conjecture of Yves André’s. Duke Mathematical Journal. 132 (2006), no. 3, 393–407. Zbl1097.11032MR2219262

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