Measured Foliations and Hilbert 12th Problem
نویسندگان
چکیده
Yu. I. Manin conjectured that the maximal abelian extensions of real quadratic number fields are generated by pseudo-lattices with multiplication. We prove this conjecture using theory measured foliations on modular curves.
منابع مشابه
Foliations of Hilbert modular surfaces
The Hilbert modular surface XD is the moduli space of Abelian varietiesA with real multiplication by a quadratic order of discriminant D > 1. The locus where A is a product of elliptic curves determines a finite union of algebraic curves XD(1) ⊂ XD. In this paper we show the lamination XD(1) extends to an essentially unique foliation FD of XD by complex geodesics. The geometry of FD is related ...
متن کاملLinking Numbers of Measured Foliations
We generalise the average asymptotic linking number of a pair of divergence-free vector fields on homology threespheres [1, 2, 14] by considering the linking of a divergence-free vector field on a manifold of arbitrary dimension with a codimension two foliation endowed with an invariant transverse measure. We prove that the average asymptotic linking number is given by an integral of Hopf type....
متن کاملMeasured Foliations and Harmonic Maps of Surfaces
Fix a Riemannian surface of negative curvature (N, h), and a differentiable surface M g of the same genus g that will host various structures. Also fix a diffeomorphism f0 : M → N . It is well known ([ES], [A], [SY1], [Sa]) that to every complex structure σ on M , there is a unique harmonic diffeomorphism f(σ) : M(σ) → (N, h) homotopic to f0 : M → N ; one is led to consider what other, possibly...
متن کاملFOLIATIONS OF HILBERT MODULAR SURFACES By CURTIS
The Hilbert modular surface XD is the moduli space of Abelian varieties A with real multiplication by a quadratic order of discriminant D > 1. The locus where A is a product of elliptic curves determines a finite union of algebraic curves XD(1) ⊂ XD. In this paper we show the lamination XD(1) extends to an essentially unique foliation FD of XD by complex geodesics. The geometry of FD is related...
متن کاملCascades in the dynamics of measured foliations
This paper studies the behavior of harmonic measured foliations on compact Riemann surfaces. Cascades in the dynamics of such a foliation can occur as its relative periods are varied. We show that in the case of genus 2, the bifurcation locus arising from such a variation is a closed, countable set of R that embeds in ω. Resumé Nous étudions le comportement des feuilletages mesurés harmoniques ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta mathematica Vietnamica
سال: 2022
ISSN: ['0251-4184', '2315-4144']
DOI: https://doi.org/10.1007/s40306-022-00479-w