Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II : tripods and combinatorial cuspidalization / Yuichiro Hoshi, Shinichi Mochizuki.
Hoshi, Yuichiro, author.; Mochizuki, Shinichi, author.
2022
QA565
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Title Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II : tripods and combinatorial cuspidalization / Yuichiro Hoshi, Shinichi Mochizuki.
Author Hoshi, Yuichiro, author.
ISBN 9789811910968 (electronic bk.)
9811910960 (electronic bk.)
9789811910951
DOI https://doi.org/10.1007/978-981-19-1096-8
Published Singapore : Springer, [2022]
Copyright ©2022
Language English
Description 1 online resource (xxiii, 150 pages).
Item Number 10.1007/978-981-19-1096-8 doi
Call Number QA565
Dewey Decimal Classification 516.3/52
Summary The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero. The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space. We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve induces the same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists. In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the étale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed May 25, 2022).
Added Author Mochizuki, Shinichi, author.
Series Lecture notes in mathematics (Springer-Verlag) ; 2299. 1617-9692
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1. Combinatorial Anabelian Geometry in the Absence of Group-theoretic Cuspidality
2. Partial Combinatorial Cuspidalization for F-admissible Outomorphisms
3. Synchronization of Tripods
4. Glueability of Combinatorial Cuspidalizations. References.

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