Mumford’s conjecture

D. Mumford conjectured in [33] that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes κi of dimension 2i. For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by BΓ∞ , where Γ∞ is the group of isotopy classes of automorphisms of a smooth oriented connected surface of “large” genus. Tillmann’s theorem [44] that the plus construction makes BΓ∞ into an infinite loop space led to a stable homotopy version of Mumford’s conjecture, stronger than the original [24]. .

100p noel_noel 17-01-2013 38 6   Download

Introduction 2. The strategy 3. Some preliminaries 3.1. Mumford-Tate groups 3.2. Variations of Z-Hodge structure on Shimura varieties 3.3. Representations of tori 4. Lower bounds for Galois orbits 4.2. Galois orbits and Mumford-Tate groups 4.3. Getting rid of G 4.4. Proof of Proposition 4.3.9 5. Images under Hecke correspondences 6. Density of Hecke orbits 7. Proof of the main result 7.3. The case where i is bounded 7.4. The case where i is not bounded 1. Introduction The aim of this article is to prove a special case of the following conjecture of Andr´ and Oort on subvarieties...

26p tuanloccuoi 04-01-2013 59 6   Download