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Openness of the Regular Locus and Generators for Module Categories

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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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Authors and Affiliations

  1. Department of Mathematics, University of Utah, Salt Lake City, UT, 84112-0090, USA

    Srikanth B. Iyengar

  2. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan

    Ryo Takahashi

  3. Department of Mathematics, University of Kansas, Lawrence, KS, 66045-7523, USA

    Ryo Takahashi

Authors
  1. Srikanth B. Iyengar
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  2. Ryo Takahashi
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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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  • DOI: https://doi.org/10.1007/s40306-018-0294-8

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