國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Bousfield classes and Ohkawa's theor...

Minami, Norihiko.

Bousfield classes and Ohkawa's theoremNagoya, Japan, August 28-30, 2015 /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Bousfield classes and Ohkawa's theoremedited by Takeo Ohsawa, Norihiko Minami.
其他題名:	Nagoya, Japan, August 28-30, 2015 /
其他作者:	Ohsawa, Takeo.
出版者:	Singapore :Springer Singapore :2020.
面頁冊數:	x, 435 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Homotopy theory.
電子資源:	https://doi.org/10.1007/978-981-15-1588-0
ISBN:	9789811515880$q(electronic bk.)

Bousfield classes and Ohkawa's theoremNagoya, Japan, August 28-30, 2015 /
Bousfield classes and Ohkawa's theoremNagoya, Japan, August 28-30, 2015 /[electronic resource] :edited by Takeo Ohsawa, Norihiko Minami. - Singapore :Springer Singapore :2020. - x, 435 p. :ill., digital ;24 cm. - Springer proceedings in mathematics & statistics,v.3092194-1009 ;. - Springer proceedings in mathematics & statistics ;v.19..

A.K. Bousfield, Foreword -- Takao Matumoto, Memories on Ohkawa's mathematical life in Hiroshima -- Carles Casacuberta, Depth and simplicity of Ohkawa's argument -- Shane Kelly, Some observations about motivic tensor triangulated geometry over a finite field -- Ruth Joachimi, Thick ideals in equivariant and motivic stable homotopy categories -- Takeo Ohsawa, Role of the L2 Method in the study of analytic Families -- Carles Casacuberta and Jiri Rosicky, Combinatorial homotopy categories -- Mark Behrens and Charles Rezk, Spectral algebra models of unstable vn-periodic homotopy theory -- Takeshi Torii, On quasi-categories of comodules and Landweber exactness -- Takuo Matsuoka, Koszul duality for En-algebras in a filtered category -- Takuo Matsuoka, Some technical aspects of factorization algebras on manifolds -- Ryo Kato, Hiroki Okajima and Katsumi Shimomura, Notes on an alegebraic stable homotopy category -- Jack Morava, Operations on integral lifts of K(n) -- Tobias Barthel, A short introduction to the telescope and chromatic splitting conjectures -- Norihiko Minami, From Ohkawa to strong generation via approximable triangulated categories - a variation on the theme of Amnon Neeman's Nagoya lecture series.

This volume originated in the workshop held at Nagoya University, August 28-30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins-Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.

ISBN: 9789811515880$q(electronic bk.)

Standard No.: 10.1007/978-981-15-1588-0doiSubjects--Topical Terms:

209299
Homotopy theory.

LC Class. No.: QA612.7 / .B687 2020

Dewey Class. No.: 514.24

Bousfield classes and Ohkawa's theoremNagoya, Japan, August 28-30, 2015 /
LDR:04144nmm a2200337 a 4500 001 572811
003 DE-He213
005 20200806114643.0
006 m d
007 cr nn 008maaau
008 200925s2020 si s 0 eng d
020 $a 9789811515880$q(electronic bk.)
020 $a 9789811515873$q(paper)
024 7 $a 10.1007/978-981-15-1588-0 $2 doi
035 $a 978-981-15-1588-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612.7 $b .B687 2020
072 7 $a PBPD $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBPD $2 thema
082 0 4 $a 514.24 $2 23
090 $a QA612.7 $b .B777 2020
245 0 0 $a Bousfield classes and Ohkawa's theorem $h [electronic resource] : $b Nagoya, Japan, August 28-30, 2015 / $c edited by Takeo Ohsawa, Norihiko Minami.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a x, 435 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer proceedings in mathematics & statistics, $x 2194-1009 ; $v v.309
505 0 $a A.K. Bousfield, Foreword -- Takao Matumoto, Memories on Ohkawa's mathematical life in Hiroshima -- Carles Casacuberta, Depth and simplicity of Ohkawa's argument -- Shane Kelly, Some observations about motivic tensor triangulated geometry over a finite field -- Ruth Joachimi, Thick ideals in equivariant and motivic stable homotopy categories -- Takeo Ohsawa, Role of the L2 Method in the study of analytic Families -- Carles Casacuberta and Jiri Rosicky, Combinatorial homotopy categories -- Mark Behrens and Charles Rezk, Spectral algebra models of unstable vn-periodic homotopy theory -- Takeshi Torii, On quasi-categories of comodules and Landweber exactness -- Takuo Matsuoka, Koszul duality for En-algebras in a filtered category -- Takuo Matsuoka, Some technical aspects of factorization algebras on manifolds -- Ryo Kato, Hiroki Okajima and Katsumi Shimomura, Notes on an alegebraic stable homotopy category -- Jack Morava, Operations on integral lifts of K(n) -- Tobias Barthel, A short introduction to the telescope and chromatic splitting conjectures -- Norihiko Minami, From Ohkawa to strong generation via approximable triangulated categories - a variation on the theme of Amnon Neeman's Nagoya lecture series.
520 $a This volume originated in the workshop held at Nagoya University, August 28-30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins-Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
650 0 $a Homotopy theory. $3 209299
650 1 4 $a Algebraic Topology. $3 273784
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology) $3 253172
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 276692
700 1 $a Ohsawa, Takeo. $3 826624
700 1 $a Minami, Norihiko. $3 860025
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer proceedings in mathematics & statistics ; $v v.19. $3 569116
856 4 0 $u https://doi.org/10.1007/978-981-15-1588-0
950 $a Mathematics and Statistics (Springer-11649)