Bousfield Classes and Ohkawa's Theorem

Bousfield Classes and Ohkawa's Theorem
Author :
Publisher : Springer Nature
Total Pages : 438
Release :
ISBN-10 : 9789811515880
ISBN-13 : 9811515883
Rating : 4/5 (80 Downloads)

Book Synopsis Bousfield Classes and Ohkawa's Theorem by : Takeo Ohsawa

Download or read book Bousfield Classes and Ohkawa's Theorem written by Takeo Ohsawa and published by Springer Nature. This book was released on 2020-03-18 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Bousfield Classes and Ohkawa's Theorem Related Books

Bousfield Classes and Ohkawa's Theorem
Language: en
Pages: 438
Authors: Takeo Ohsawa
Categories: Mathematics
Type: BOOK - Published: 2020-03-18 - Publisher: Springer Nature

DOWNLOAD EBOOK

This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfiel
Homotopy Invariant Algebraic Structures
Language: en
Pages: 392
Authors: Jean-Pierre Meyer
Categories: Mathematics
Type: BOOK - Published: 1999 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditiona
Axiomatic, Enriched and Motivic Homotopy Theory
Language: en
Pages: 396
Authors: John Greenlees
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The NATO Advanced Study Institute "Axiomatic, enriched and rna tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambrid
Geometric and Topological Aspects of the Representation Theory of Finite Groups
Language: en
Pages: 493
Authors: Jon F. Carlson
Categories: Mathematics
Type: BOOK - Published: 2018-10-04 - Publisher: Springer

DOWNLOAD EBOOK

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at th
Stable Homotopy over the Steenrod Algebra
Language: en
Pages: 193
Authors: John Harold Palmieri
Categories: Mathematics
Type: BOOK - Published: 2001 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This title applys the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A DEGREES{*}$. More precisely, let $A$ be the d