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Eventually homological isomorphisms and Gorenstein projective modules

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Abstract

We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories, Gorenstein defect categories and stable categories of Gorenstein projective modules. Furthermore, we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms. Applying these results to arrow removal and vertex removal, we describe the Gorenstein projective modules over some non-monomial algebras, and verify the Auslander-Reiten conjecture for certain algebras.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 12061060 and 11801141), the Scientific and Technological Planning Project of Yunnan Province (Grant No. 202305AC160005) and the Scientific and Technological Innovation Team of Yunnan Province (Grant No. 2020CXTD25). The authors thank the referees for their helpful comments.

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Authors and Affiliations

  1. School of Mathematics, Yunnan Normal University, Kunming, 650500, China

    Yongyun Qin

  2. School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China

    Dawei Shen

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  1. Yongyun Qin
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  2. Dawei Shen
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Correspondence to Yongyun Qin.

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Qin, Y., Shen, D. Eventually homological isomorphisms and Gorenstein projective modules. Sci. China Math. (2023). https://doi.org/10.1007/s11425-022-2146-5

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