The Algebraic and Anabelian Geometry of Configuration Spaces
نویسندگان
چکیده
In this paper, we study the pro-Σ fundamental groups of configuration spaces, where Σ is either the set of all prime numbers or a set consisting of a single prime number. In particular, we show, via two somewhat distinct approaches, that, in many cases, the “fiber subgroups” of such fundamental groups arising from the various natural projections of a configuration space to lower-dimensional configuration spaces may be characterized group-theoretically.
منابع مشابه
Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves Ii: Tripods and Combinatorial Cuspidalization
Let Σ be a subset of the set of prime numbers which is either equal to the entire set of prime numbers or of cardinality one. In the present paper, we continue our study of the pro-Σ fundamental groups of hyperbolic curves and their associated configuration spaces over algebraically closed fields in which the primes of Σ are invertible. The starting point of the theory of the present paper is a...
متن کاملStatement Aaron Silberstein 1
Anabelian geometry is a grand synthesis of number theory, algebraic geometry, algebraic topology, and group theory. Parallel to the situation in algebraic topology where to a space, one attaches a fundamental group (after fixing a basepoint), in algebraic geometry one attaches to every algebraic variety X (and a geometric point x) its étale fundamental group πét 1 (X,x). Similar to the topologi...
متن کاملIntroduction 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 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 کاملAnabelian geometry and descent obstructions on moduli spaces
We study the section conjecture of anabelian geometry and the sufficiency of the finite descent obstruction to the Hasse principle for the moduli spaces of principally polarized abelian varieties and of curves over number fields. For the former we show that both the section conjecture and the finite descent obstruction fail in a very controlled way. For the latter, we prove some partial results...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006