Global Solvably Closed Anabelian Geometry
نویسندگان
چکیده
In this paper, we study the pro-Σ anabelian geometry of hyperbolic curves, where Σ is a nonempty set of prime numbers, over Galois groups of “solvably closed extensions” of number fields — i.e., infinite extensions of number fields which have no nontrivial abelian extensions. The main results of this paper are, in essence, immediate corollaries of the following three ingredients: (a) classical results concerning the structure of Galois groups of number fields; (b) an anabelian result of Uchida concerning Galois groups of solvably closed extensions of number fields; (c) a previous result of the author concerning the pro-Σ anabelian geometry of hyperbolic curves over nonarchimedean local fields.
منابع مشابه
Introduction to Birational Anabelian Geometry
We survey recent developments in the Birational Anabelian Geometry program aimed at the reconstruction of function fields of algebraic varieties over algebraically closed fields from pieces of their absolute Galois groups.
متن کاملAnabelian Intersection Theory I: the Conjecture of Bogomolov-pop and Applications
A. Grothendieck first coined the term “anabelian geometry” in a letter to G. Faltings [Gro97a] as a response to Faltings’ proof of the Mordell conjecture and in his celebrated Esquisse d’un Programme [Gro97b]. The “yoga” of Grothendieck’s anabelian geometry is that if the étale fundamental group πét 1 pX,xq of a variety X at a geometric point x is rich enough, then it should encode much of the ...
متن کاملTopics in Absolute Anabelian Geometry Ii: Decomposition Groups and Endomorphisms
The present paper, which forms the second part of a three-part series in which we study absolute anabelian geometry from an algorithmic point of view, focuses on the study of the closely related notions of decomposition groups and endomorphisms in this anabelian context. We begin by studying an abstract combinatorial analogue of the algebro-geometric notion of a stable polycurve [i.e., a “succe...
متن کاملPro-` Abelian-by-central Galois Theory of Zariski Prime Divisors
In the present paper I show that one can recover much of the inertia structure of Zariski (quasi) divisors of a function field K|k over an algebraically closed base field k from the maximal pro-` abelian-by-central Galois theory of K. The results play a central role in the birational anabelian geometry and related questions.
متن کاملPro-` Abelian-by-central Galois Theory of Prime Divisors
In the present paper I show that one can recover much of the inertia structure of (quasi) divisors of a function field K|k over an algebraically closed base field k from the maximal pro-` abelian-by-central Galois theory of K. The results play a central role in the birational anabelian geometry and related questions.
متن کامل