On the Auslander–Reiten conjecture for Cohen–Macaulay local rings
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- by Shiro Goto and Ryo Takahashi PDF
- Proc. Amer. Math. Soc. 145 (2017), 3289-3296 Request permission
Abstract:
This paper studies vanishing of Ext modules over Cohen–Macaulay local rings. The main result of this paper implies that the Auslander–Reiten conjecture holds for maximal Cohen–Macaulay modules of rank one over Cohen–Macaulay normal local rings. It also recovers a theorem of Avramov–Buchweitz–Şega and Hanes–Huneke, which shows that the Tachikawa conjecture holds for Cohen–Macaulay generically Gorenstein local rings.References
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Additional Information
- Shiro Goto
- Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan
- MR Author ID: 192104
- Email: goto@math.meiji.ac.jp, shirogoto@gmail.com
- Ryo Takahashi
- Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi 464-8602, Japan
- MR Author ID: 674867
- Email: takahashi@math.nagoya-u.ac.jp
- Received by editor(s): March 1, 2016
- Received by editor(s) in revised form: September 9, 2016
- Published electronically: February 20, 2017
- Additional Notes: The first author was partly supported by JSPS Grant-in-Aid for Scientific Research (C) 25400051. The second author was partly supported by JSPS Grant-in-Aid for Scientific Research (C) 25400038.
- Communicated by: Jerzy Weyman
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3289-3296
- MSC (2010): Primary 13D22, 13H10
- DOI: https://doi.org/10.1090/proc/13487
- MathSciNet review: 3652783