On a question of Buchweitz about ranks of syzygies of modules of finite length

Toshinori Kobayashi

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arXiv · 1701.04990

On a question of Buchweitz about ranks of syzygies of modules of finite length

Toshinori Kobayashi

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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 question is affrmative, then R is a hypersurface. If moreover R has dimension two, then we show that the converse also holds true.

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Toshinori Kobayashi. 2017-01-18. On a question of Buchweitz about ranks of syzygies of modules of finite length. https://arxiv.org/abs/1701.04990

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