The André-Oort conjecture

Abstract

In this paper we prove, assuming the Generalized Riemann Hypothesis, the André-Oort conjecture on the Zariski closure of sets of special points in a Shimura variety.In the case of sets of special points satisfying an additional assumption, we prove the conjecture without assuming the GRH. ContentsB. KLINGLER and A. YAFAEV 5. Degrees on Shimura varieties 888 5.1.Degrees 888 5.2.Nefness 889 5.3.Baily-Borel compactification 889 6. Inclusion of Shimura subdata 894 7. The geometric criterion 896 7.1.Hodge genericity 896 7.2.The criterion 897 8. Existence of suitable Hecke correspondences 903 8.1.Iwahori subgroups 904 8.2.A uniformity result 907 8.3.Proof of Theorem 8.1 908 9. Conditions on the prime l 910 9.1.Situation 910 9.2.The criterion 911 10.The choice of a prime l 916 10.1.Effective Chebotarev 916 10.2.Proof of Theorem 3.2.

Locations

• Annals of Mathematics - View - PDF