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arXiv · 2411.05356

Lambda-pure global dimension of Grothendieck categories and some applications

Xi Wang·Hailou Yao·Lei Shen
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Abstract

We study the $\lambda$-pure global dimension of a Grothendieck category $\cal A$, and provide two different applications about this dimension. We obtain that if the $\lambda$-pure global dimension $\plgldA<\infty$, then (1) The ordinary bounded derived category (where $\cal A$ has enough projective objects) and the bounded $\lambda$-pure one differ only by a homotopy category; (2) The $\lambda$-pure singularity category $\DlsgA =0$. At last, we explore the reason why the general construction of classic Buchweitz-Happel Theorem is not feasible for $\lambda$-pure one.

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Xi Wang, Hailou Yao, Lei Shen. 2024-11-08. Lambda-pure global dimension of Grothendieck categories and some applications. https://arxiv.org/abs/2411.05356

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