Unstable elements in cohomology and a question of Lescot
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912511842844672 |
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| author | Iyengar, Srikanth B. Maitra, Sarasij Tribone, Tim |
| author_facet | Iyengar, Srikanth B. Maitra, Sarasij Tribone, Tim |
| contents | In his work on the Bass series of syzygy modules of modules over a commutative noetherian local ring $R$, Lescot introduces a numerical invariant, denoted $σ(R)$, and asks whether it is finite for any $R$. He proves that this is so when $R$ is Gorenstein or Golod. In the present work many new classes of rings $R$ for which $σ(R)$ is finite are identified. The new insight is that $σ(R)$ is related to the natural map from the usual cohomology of the module to its stable cohomology, which permits the use of multiplicative structures to study the question of finiteness of $σ(R)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_23213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unstable elements in cohomology and a question of Lescot Iyengar, Srikanth B. Maitra, Sarasij Tribone, Tim Commutative Algebra 13D02, 13D07 In his work on the Bass series of syzygy modules of modules over a commutative noetherian local ring $R$, Lescot introduces a numerical invariant, denoted $σ(R)$, and asks whether it is finite for any $R$. He proves that this is so when $R$ is Gorenstein or Golod. In the present work many new classes of rings $R$ for which $σ(R)$ is finite are identified. The new insight is that $σ(R)$ is related to the natural map from the usual cohomology of the module to its stable cohomology, which permits the use of multiplicative structures to study the question of finiteness of $σ(R)$. |
| title | Unstable elements in cohomology and a question of Lescot |
| topic | Commutative Algebra 13D02, 13D07 |
| url | https://arxiv.org/abs/2507.23213 |