東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ subject:"Abelian categories." ]

切換: 標籤 | MARC模式 | ISBD

Topics surrounding the combinatorial...

Hoshi, Yuichiro.

FindBook

Google Book

Amazon

博客來

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II = tripods and combinatorial cuspidalization /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II/ by Yuichiro Hoshi, Shinichi Mochizuki.
其他題名:	tripods and combinatorial cuspidalization /
作者:	Hoshi, Yuichiro.
其他作者:	Mochizuki, Shinichi.
出版者:	Singapore :Springer Nature Singapore : : 2022.,
面頁冊數:	xxiii, 150 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Curves, Algebraic. -
電子資源:	https://doi.org/10.1007/978-981-19-1096-8
ISBN:	9789811910968

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II = tripods and combinatorial cuspidalization /
Hoshi, Yuichiro.

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves IItripods and combinatorial cuspidalization /[electronic resource] :by Yuichiro Hoshi, Shinichi Mochizuki. - Singapore :Springer Nature Singapore :2022. - xxiii, 150 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 22991617-9692 ;. - Lecture notes in mathematics ;v. 2299..

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.

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 etale 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.

ISBN: 9789811910968

Standard No.: 10.1007/978-981-19-1096-8doiSubjects--Topical Terms:

540522
Curves, Algebraic.

LC Class. No.: QA565 / .H67 2022

Dewey Class. No.: 516.352

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II = tripods and combinatorial cuspidalization /
LDR:03401nmm a2200337 a 4500 001 2300728
003 DE-He213
005 20220520205744.0
006 m d
007 cr nn 008maaau
008 230324s2022 si s 0 eng d
020 $a 9789811910968 $q (electronic bk.)
020 $a 9789811910951 $q (paper)
024 7 $a 10.1007/978-981-19-1096-8 $2 doi
035 $a 978-981-19-1096-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA565 $b .H67 2022
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 516.352 $2 23
090 $a QA565 $b .H825 2022
100 1 $a Hoshi, Yuichiro. $3 3599513
245 1 0 $a Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II $h [electronic resource] : $b tripods and combinatorial cuspidalization / $c by Yuichiro Hoshi, Shinichi Mochizuki.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2022.
300 $a xxiii, 150 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2299
505 0 $a 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.
520 $a 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 etale 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.
650 0 $a Curves, Algebraic. $3 540522
650 0 $a Abelian categories. $3 705107
650 1 4 $a Number Theory. $3 891078
650 2 4 $a Algebraic Geometry. $3 893861
700 1 $a Mochizuki, Shinichi. $3 728361
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2299. $3 3599514
856 4 0 $u https://doi.org/10.1007/978-981-19-1096-8
950 $a Mathematics and Statistics (SpringerNature-11649)