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Endofunctors of singularity categories characterizing Gorenstein rings


Authors: Takuma Aihara and Ryo Takahashi
Journal: Proc. Amer. Math. Soc. 143 (2015), 3777-3779
MSC (2010): Primary 13D09, 13H10, 18E30
DOI: https://doi.org/10.1090/proc/12580
Published electronically: April 29, 2015
MathSciNet review: 3359569
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove that certain contravariant endofunctors of singularity categories characterize Gorenstein rings.


References [Enhancements On Off] (What's this?)

  • [1] Maurice Auslander and Mark Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, R.I., 1969. MR 0269685
  • [2] R.-O. Buchweitz, Maximal Cohen-Macaulay modules and Tate-cohomology over Gorenstein rings, Preprint (1986), http://hdl.handle.net/1807/16682.

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Additional Information

Takuma Aihara
Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi 464-8602, Japan
Address at time of publication: Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan
Email: aihara@las.osakafu-u.ac.jp

Ryo Takahashi
Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi 464-8602, Japan
Email: takahashi@math.nagoya-u.ac.jp

DOI: https://doi.org/10.1090/proc/12580
Keywords: Singularity category, stable category of Cohen--Macaulay modules, Gorenstein ring, Cohen--Macaulay ring
Received by editor(s): May 18, 2014
Published electronically: April 29, 2015
Additional Notes: The first author was partly supported by IAR Research Project, Institute for Advanced Research, Nagoya University.
The second author was partly supported by JSPS Grant-in-Aid for Scientific Research (C) 25400038
Communicated by: Irena Peeva
Article copyright: © Copyright 2015 American Mathematical Society