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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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 29, 1089–1097 (2021). https://doi.org/10.1007/s10485-021-09648-8
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DOI: https://doi.org/10.1007/s10485-021-09648-8
Keywords
- Tensor triangulated category
- Triangular spectrum
- Singularity category
- Semi-orthogonal decomposition
- Finite EI category
- Category algebra