Counting Manifolds and Class Field Towers
نویسندگان
چکیده
In [BGLM] and [GLNP] it was conjectured that if H is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in H of covolume at most x is x log x/ log log x where γ(H) is an explicit constant computable from the (absolute) root system of H . In this paper we prove that this conjecture is false. In fact, we show that the growth is at rate x log . A crucial ingredient of the proof is the existence of towers of field extensions with bounded root discriminant which follows from the seminal work of Golod and Shafarevich on class field towers.
منابع مشابه
Three-manifolds Class Field Theory (homology of Coverings for a Non-virtually Haken Manifold)
Introduction 2 1. Preliminary results in group cohomology 4 2. Free Zp-action in three-manifolds 7 3. Free Zp⊕Zp-action in three-manifolds 8 4. Algebraic study of linking forms 12 5. Linking forms and transfer nonvanishing theorem 13 6. The structure of anisotropic extensions, I 14 7. Shrinking 16 8. Isotropic extension 17 9. Blowing upH1: the non-abelian step 18 10. Class towers and the struct...
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