Correspondences on Hyperbolic Curves
نویسنده
چکیده
We consider hyperbolic curves over an algebraically closed field k of characteristic zero. We call two such curves X, Y isogenous if there exists a nonempty scheme C , together with finite étale morphisms C → X, C → Y . (We refer to such a pair (C → X,C → Y ) as a correspondence from X to Y .) It is easy to see that the relation of isogeny is an equivalence relation on the set of isomorphism classes of hyperbolic curves over k. Then the first main result of this paper (cf. Lemma 4.1 and Theorem 4.2 in the text) is the following:
منابع مشابه
Contractive Curves
We discuss the dynamics of the correspondences associated to those plane curves whose local sections contract the Poincaré metric in a hyperbolic planar domain. 1. Introduction. We consider certain 1-dimensional, holomorphic correspondences of hyperbolic type, which we call " contractive curves. " These are curves whose local sections contract the Poincaré metric of a hyperbolic planar domain. ...
متن کاملSelf-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups
An integral hyperbolic lattice is called reflective if its automorphism group is generated by reflections, up to finite index. Since 1981, it is known that their number is essentially finite. We show that K3 surfaces X over C with reflective Picard lattices can be characterized in terms of compositions of their self-correspondences via moduli of sheaves with primitive isotropic Mukai vector: Th...
متن کاملGalois Sections in Absolute Anabelian Geometry
In this paper, we continue our study of the absolute anabelian geometry of hyperbolic curves over p-adic local fields [i.e., finite extensions of the field of p-adic numbers, for some prime number p], begun in [Mzk2], [Mzk3]. In [Mzk3], Theorem 2.4, it was shown, as a consequence of the main theorem of [Mzk1], that certain categories of finite étale correspondences associated to a hyperbolic cu...
متن کاملNonrigid Point Correspondence Recovery for Planar Curves Using Fourier Decomposition
A novel method of point correspondence recovery between planar curves is presented in this paper where motion between the curves is nonrigid. Fourier transformation is used to decompose planar curves into a set of ellipses, each at a different frequency level. The point correspondences between two planar curves is based on the correspondences between two ellipses in the same frequency level. At...
متن کاملRims-1750 on the Cuspidalization Problem for Hyperbolic Curves over Finite Fields
In this paper, we study some group-theoretic constructions associated to arithmetic fundamental groups of hyperbolic curves over finite fields. One of the main results of this paper asserts that any Frobeniuspreserving isomorphism between the geometrically pro-l fundamental groups of hyperbolic curves with one given point removed induces an isomorphism between the geometrically pro-l fundamenta...
متن کامل