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math.CTJul 1, 2017
19
citations (OpenAlex)
authors
  • Paul Balmer
  • Henning Krause
  • Greg Stevenson
institutions
  • Bielefeld University
  • University of California, Los Angeles
  • University of Glasgow
arXiv abstractPDF
paper

Tensor-triangular fields: Ruminations

arXiv:1707.02167 · doi:10.1007/s00029-019-0454-2

Abstract

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.

32 pages

References in corpus (1)

  • The frame of smashing tensor-ideals

Cited by in corpus (11)

  • Nilpotence theorems via homological residue fields
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  • Computing homological residue fields in algebra and topology
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  • Duality pairs, phantom maps, and definability in triangulated categories
  • Support theory for Drinfeld doubles of some infinitesimal group schemes
  • The shift-homological spectrum and parametrising kernels of rank functions
  • Definable functors between triangulated categories
  • Telescope conjecture via homological residue fields with applications to schemes
  • Homological stratification and descent
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