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001446972 001__ 1446972
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001446972 020__ $$a9789811910968$$q(electronic bk.)
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001446972 0247_ $$a10.1007/978-981-19-1096-8$$2doi
001446972 035__ $$aSP(OCoLC)1319856706
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001446972 08204 $$a516.3/52$$223/eng/20220525
001446972 1001_ $$aHoshi, Yuichiro,$$eauthor.
001446972 24510 $$aTopics surrounding the combinatorial anabelian geometry of hyperbolic curves II :$$btripods and combinatorial cuspidalization /$$cYuichiro Hoshi, Shinichi Mochizuki.
001446972 24630 $$aTripods and combinatorial cuspidalization
001446972 264_1 $$aSingapore :$$bSpringer,$$c[2022]
001446972 264_4 $$c©2022
001446972 300__ $$a1 online resource (xxiii, 150 pages).
001446972 336__ $$atext$$btxt$$2rdacontent
001446972 337__ $$acomputer$$bc$$2rdamedia
001446972 338__ $$aonline resource$$bcr$$2rdacarrier
001446972 4901_ $$aLecture notes in mathematics,$$x1617-9692 ;$$vvolume 2299
001446972 504__ $$aIncludes bibliographical references.
001446972 5050_ $$a1. 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.
001446972 506__ $$aAccess limited to authorized users.
001446972 520__ $$aThe 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.
001446972 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed May 25, 2022).
001446972 650_0 $$aCurves, Algebraic.
001446972 650_0 $$aAbelian categories.
001446972 655_0 $$aElectronic books.
001446972 7001_ $$aMochizuki, Shinichi,$$eauthor.
001446972 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2299.$$x1617-9692
001446972 852__ $$bebk
001446972 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-19-1096-8$$zOnline Access$$91397441.1
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001446972 983__ $$aOnline
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