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arXiv · 1905.02329

On pure derived and pure singularity categories

Tianya Cao·Wei Ren
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Abstract

Firstly, we compare the bounded derived categories with respect to the pure-exact and the usual exact structures, and describe bounded derived category by pure-projective modules, under a fairly strong assumption on the ring. Then, we study Verdier quotient of bounded pure derived category modulo the bounded homotopy category of pure-projective modules, which is called a pure singularity category since we show that it reflects the finiteness of pure-global dimension of rings. Moreover, invariance of pure singularity in a recollement of bounded pure derived categories is studied.

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Tianya Cao, Wei Ren. 2019-05-07. On pure derived and pure singularity categories. https://doi.org/10.1142/s0219498820501170

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