Openness of the Regular Locus and Generators for Module Categories

Abstract

This work clarifies the relationship between the openness of the regular locus of a commutative Noetherian ring R and the existence of generators for the category of finitely generated R-modules, the corresponding bounded derived category, and for the singularity category of R.

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Acknowledgements

The authors are grateful to Shiro Goto, Kazuhiko Kurano, and Jun-ichi Nishimura for valuable suggestions. Finally, the authors thank the referee for reading the paper carefully and giving helpful comments.

Funding

The first author was partially supported by the National Science Foundation, under grant DMS-1700985. The second author was partially supported by JSPS Grant-in-Aid for Scientific Research 16K05098 and JSPS Fund for the Promotion of Joint International Research 16KK0099.

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Correspondence to Ryo Takahashi.

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Iyengar, S.B., Takahashi, R. Openness of the Regular Locus and Generators for Module Categories. Acta Math Vietnam 44, 207–212 (2019). https://doi.org/10.1007/s40306-018-0294-8

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Keywords

  • Bounded derived category
  • Generator
  • Module category
  • Regular locus
  • Singularity category

Mathematics Subject Classification (2010)

  • 13D09
  • 13B22