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Tensor-triangular fields: ruminations

  • Paul Balmer
  • Henning Krause
  • Greg StevensonEmail author
Open Access


We examine the concept of field in tensor-triangular geometry. We gather examples and discuss possible approaches, while highlighting open problems. As the construction of residue tt-fields remains elusive, we instead produce suitable homological tensor-functors to Grothendieck categories.


Residue field tt-Geometry Module category 

Mathematics Subject Classification

18E30 (20J05, 55U35) 



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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Mathematics DepartmentUCLALos AngelesUSA
  2. 2.Universität Bielefeld, Fakultät für MathematikBielefeldGermany
  3. 3.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK

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