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PIMS Summer School and Workshop

PSSW 2016: Geometric and Topological Aspects of the Representation Theory of Finite Groups pp 393–405Cite as

Complete Boolean Algebras are Bousfield Lattices

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 242))

Abstract

Given a complete Heyting algebra, we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given Heyting algebra. As a consequence, we deduce that any complete Boolean algebra is the Bousfield lattice of some tensor triangulated category. Using the same ideas, we then give two further examples illustrating some interesting behaviour of the Bousfield lattice.

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References

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Acknowledgements

I am thankful to the referee for their careful reading of the manuscript; they provided several helpful comments which resulted in improvements to the exposition.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8SQ, UK

    Greg Stevenson

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  1. Greg Stevenson
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Correspondence to Greg Stevenson .

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Editors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, USA

    Jon F. Carlson

  2. Department of Mathematics, University of Utah, Salt Lake City, UT, USA

    Srikanth B. Iyengar

  3. Department of Mathematics, University of Washington, Seattle, WA, USA

    Julia Pevtsova

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Stevenson, G. (2018). Complete Boolean Algebras are Bousfield Lattices. In: Carlson, J., Iyengar, S., Pevtsova, J. (eds) Geometric and Topological Aspects of the Representation Theory of Finite Groups. PSSW 2016. Springer Proceedings in Mathematics & Statistics, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-319-94033-5_16

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