The mapping cone of an Eisenbud operator and applications to exact zero divisors
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929282119368704 |
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| author | Şega, Liana M. Sireeshan, Deepak |
| author_facet | Şega, Liana M. Sireeshan, Deepak |
| contents | Let $(Q,\mathfrak{m},{\sf k})$ be a local ring that admits an exact pair of zero divisors $(f,g)$, $M$ a $Q$-module with $fM = 0$ and $U$ a free resolution of $M$ over $Q$. We construct a degree $-2$ chain map, which we call an Einsenbud operator, on the complex $U \otimes_Q Q/(f,g)$ and use the mapping cone of the operator to study two exact sequences that relate homology over $Q$ to homology over $Q/(f)$. Several applications are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The mapping cone of an Eisenbud operator and applications to exact zero divisors Şega, Liana M. Sireeshan, Deepak Commutative Algebra Let $(Q,\mathfrak{m},{\sf k})$ be a local ring that admits an exact pair of zero divisors $(f,g)$, $M$ a $Q$-module with $fM = 0$ and $U$ a free resolution of $M$ over $Q$. We construct a degree $-2$ chain map, which we call an Einsenbud operator, on the complex $U \otimes_Q Q/(f,g)$ and use the mapping cone of the operator to study two exact sequences that relate homology over $Q$ to homology over $Q/(f)$. Several applications are given. |
| title | The mapping cone of an Eisenbud operator and applications to exact zero divisors |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2403.12458 |