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Springer Proceedings in Mathematics & Statistics

Bousfield Classes and Ohkawa's Theorem

Nagoya, Japan, August 28-30, 2015

Editors: Ohsawa, Takeo, Minami, Norihiko (Eds.)

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  • Is the world's first volume that focuses on the surprising and mysterious Ohkawa's theorem: the Bousfield classes form a set
  • Starts with Ohkawa's theorem, stated in the universal stable homotopy category, and narrates an inspiring, extensive mathematical story
  • Contains experts’ surveys including motivic and chromatic homotopy theories, higher categorical applications, derived categories, and L2 methods of algebraic geometry
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About this book

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.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-981-15-1588-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-981-15-1587-3
  • Free shipping for individuals worldwide
  • Immediate ebook access* with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bousfield Classes and Ohkawa's Theorem
Book Subtitle
Nagoya, Japan, August 28-30, 2015
Editors
  • Takeo Ohsawa
  • Norihiko Minami
Series Title
Springer Proceedings in Mathematics & Statistics
Series Volume
309
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-1588-0
DOI
10.1007/978-981-15-1588-0
Hardcover ISBN
978-981-15-1587-3
Series ISSN
2194-1009
Edition Number
1
Number of Pages
X, 435
Number of Illustrations
8 b/w illustrations, 1 illustrations in colour
Topics

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