Editors:
- 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
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 309)
Conference series link(s): BouCla: International Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa
Conference proceedings info: BouCla 2015.
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Table of contents (14 papers)
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Front Matter
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 Smithin 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 storyand 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.
Editors and Affiliations
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Graduate School of Mathematics, Nagoya University, Nagoya, Japan
Takeo Ohsawa
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Department of Computer Science, Nagoya Institute of Technology, Nagoya, Japan
Norihiko Minami
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
DOI: https://doi.org/10.1007/978-981-15-1588-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2020
Hardcover ISBN: 978-981-15-1587-3Published: 19 March 2020
Softcover ISBN: 978-981-15-1590-3Published: 19 March 2021
eBook ISBN: 978-981-15-1588-0Published: 18 March 2020
Series ISSN: 2194-1009
Series E-ISSN: 2194-1017
Edition Number: 1
Number of Pages: X, 435
Topics: Algebraic Topology, Manifolds and Cell Complexes (incl. Diff.Topology), Several Complex Variables and Analytic Spaces