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International Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa

BouCla 2015: Bousfield Classes and Ohkawa's Theorem pp 3–15Cite as

Depth and Simplicity of Ohkawa’s Argument

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 309))

Abstract

This is an expository article about Ohkawa’s theorem stating that acyclic classes of representable homology theories form a set. We provide background in stable homotopy theory and an overview of subsequent advances in the study of Bousfield lattices. As a new result, we prove that there is a proper class of acyclic classes of nonrepresentable homology theories.

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Acknowledgements

The author wishes to acknowledge the kind hospitality of the University of Nagoya during the memorial conference for Professor Ohkawa held in August 2015. The content of Sect. 7 is based on joint work of the author with Pau Casassas and Fernando Muro. The author was supported by the Agency for Management of University and Research Grants of Catalonia with references 2014 SGR 114 and 2017 SGR 585, and the Spanish Ministry of Economy and Competitiveness under AEI/FEDER research grants MTM2013-42178-P and MTM2016-76453-C2-2-P, as well as grant MDM-2014-0445 awarded to the Barcelona Graduate School of Mathematics.

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Authors and Affiliations

  1. Facultat de Matemàtiques i Informàtica, Universitat de Barcelona (UB), Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain

    Carles Casacuberta

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  1. Carles Casacuberta
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Correspondence to Carles Casacuberta .

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Editors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, Aichi, Japan

    Takeo Ohsawa

  2. Department of Computer Science, Nagoya Institute of Technology, Nagoya, Japan

    Norihiko Minami

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Casacuberta, C. (2020). Depth and Simplicity of Ohkawa’s Argument. In: Ohsawa, T., Minami, N. (eds) Bousfield Classes and Ohkawa's Theorem. BouCla 2015. Springer Proceedings in Mathematics & Statistics, vol 309. Springer, Singapore. https://doi.org/10.1007/978-981-15-1588-0_2

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