On the combinatorial anabelian geometry of nodally nondegenerate outer representations
نویسندگان
چکیده
منابع مشابه
On the Combinatorial Anabelian Geometry of Nodally Nondegenerate Outer Representations
Let Σ be a nonempty set of prime numbers. In the present paper, we continue the study, initiated in a previous paper by the second author, of the combinatorial anabelian geometry of semi-graphs of anabelioids of pro-Σ PSC-type, i.e., roughly speaking, semi-graphs of anabelioids associated to pointed stable curves. Our first main result is a partial generalization of one of the main combinatoria...
متن کاملTopics 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 کاملDeformation of Outer Representations of Galois Group
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...
متن کاملOn the ‘Section Conjecture’ in anabelian geometry
Let X be a smooth projective curve of genus > 1 over a field K with function field K(X), let π1(X) be the arithmetic fundamental group of X over K and let GF denote the absolute Galois group of a field F . The section conjecture in Grothendieck’s anabelian geometry says that the sections of the canonical projection π1(X) → GK are (up to conjugation) in one-to-one correspondence with the K-ratio...
متن کاملThe Absolute Anabelian Geometry of Canonical Curves
In this paper, we continue our study of the issue of the extent to which a hyperbolic curve over a finite extension of the field of p-adic numbers is determined by the profinite group structure of its étale fundamental group. Our main results are that: (i) the theory of correspondences of the curve — in particular, its arithmeticity — is completely determined by its fundamental group; (ii) when...
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: Hiroshima Mathematical Journal
سال: 2011
ISSN: 0018-2079
DOI: 10.32917/hmj/1323700038