Thick Subcategories of the Relative Stable Category

Carlson, Jon

doi:10.1007/978-3-319-94033-5_2

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…The following corollary recovers our original inspiration[BS19, Theorem 3.4]. Compare also[Car18, Proposition 6.3] in modular representation theory.5.10. Corollary.…”

supporting

confidence: 65%

“…It turns out that there can be many of the former, non-K-triangulated, variety and that the lattices can exhibit starkly divergent behaviors. The following construction hints at this and was discovered by Jon Carlson in representation theory, see [Car18]. 5.13.…”

Section: * * *mentioning

confidence: 84%

“…in modular representation theory, for instance in [CPW98]. In recent years, those categories have generated renewed interest, in connection with cluster algebras [Jør10], around Broué's conjecture [WZ18] or even closer to tensor-triangular geometry in [BCS19, BS19,Car18].…”

Section: Introductionmentioning

confidence: 99%

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Relative stable categories and birationality

Balmer¹,

Stevenson

2021

J. London Math. Soc.

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We propose a general method to construct new triangulated categories, relative stable categories, as additive quotients of a given one. This construction enhances results of Beligiannis, particularly in the tensor-triangular setting. We prove a birationality result showing that the original category and its relative stable quotient are equivalent on some open piece of their spectrum. Contents 1. Introduction 1 2. Preliminaries 4 3. Proper classes of triangles 5 4. Beligiannis' construction 9 5. Thick subcategories and proto-birationality 15 6. Algebraicity 19 7. Tensor-triangulated stable categories 21 8. Thick tensor-ideals and birationality 25 References 29

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“…The following corollary recovers our original inspiration[BS19, Theorem 3.4]. Compare also[Car18, Proposition 6.3] in modular representation theory.5.10. Corollary.…”

supporting

confidence: 65%

Section: * * *mentioning

confidence: 84%