Spectra of Tensor Triangulated Categories over a Category Algebra—A New Approach

Abstract

We provide a new method to compute the Balmer spectra of the bounded derived category and the singularity category of the category algebra of a finite EI category by a decomposition trick due to Stevenson. In particular, we reobtain the result on the singularity category given by Wang under a weaker condition.

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Acknowledgements

I would like to thank professor Changchang Xi for introducing me to the theory of tensor triangular geometry. I like to thank professor Hongxing Chen and the anonymous referee who carefully read my work and provided insightful comments which helped me improve the paper.

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Correspondence to Yaohua Zhang.

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Communicated by Henning Krause.

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Zhang, Y. Spectra of Tensor Triangulated Categories over a Category Algebra—A New Approach. Appl Categor Struct (2021). https://doi.org/10.1007/s10485-021-09648-8

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Keywords

  • Tensor triangulated category
  • Triangular spectrum
  • Singularity category
  • Semi-orthogonal decomposition
  • Finite EI category
  • Category algebra

Mathematics Subject Classification

  • Primary: 18D10
  • 18E30
  • Secondary: 16D90
  • 16E35
  • 16G10