On a question of Buchweitz about ranks of syzygies of modules of finite length
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- by Toshinori Kobayashi PDF
- Proc. Amer. Math. Soc. 147 (2019), 455-460 Request permission
Abstract:
Let $R$ be a local ring of dimension $d$. Buchweitz asks if the rank of the $d$th syzygy of a module of finite lengh is greater than or equal to the rank of the $d$th syzygy of the residue field, unless the module has finite projective dimension. Assuming that $R$ is Gorenstein, we prove that if the answer is affirmative, then $R$ is a hypersurface. If moreover $R$ has dimension two, then we show that the converse also holds true.References
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Additional Information
- Toshinori Kobayashi
- Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi 464-8602, Japan
- MR Author ID: 1229546
- Email: m16021z@math.nagoya-u.ac.jp
- Received by editor(s): January 18, 2017
- Received by editor(s) in revised form: June 11, 2017
- Published electronically: November 8, 2018
- Communicated by: Jerzy Weyman
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 455-460
- MSC (2010): Primary 13C14, 13D02, 13H10
- DOI: https://doi.org/10.1090/proc/14252
- MathSciNet review: 3894883