Multiple Tor modules: rigidity and Mayer-Vietoris spectral sequences
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910157491929088 |
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| author | Banerjee, Arindam Chardin, Marc Holanda, Rafael |
| author_facet | Banerjee, Arindam Chardin, Marc Holanda, Rafael |
| contents | We extend some properties of a pair of ideals described in terms of Tor modules to any number of ideals, including the well-known rigidity property. Those extensions require the development of a homological theory for spectral sequences arising from multiple complexes. Out of this theory, two new complexes associated with quotients by sums and quotients by products of the given ideals emerge, and their homologies are related via the Tor-independence property. In the multigraded setting, we describe the support regions of Tor modules for quotients by sums and products of ideals generated by variables in terms of each other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiple Tor modules: rigidity and Mayer-Vietoris spectral sequences Banerjee, Arindam Chardin, Marc Holanda, Rafael Commutative Algebra 13D02, 18G40 (Primary), 13C12 (Secondary) We extend some properties of a pair of ideals described in terms of Tor modules to any number of ideals, including the well-known rigidity property. Those extensions require the development of a homological theory for spectral sequences arising from multiple complexes. Out of this theory, two new complexes associated with quotients by sums and quotients by products of the given ideals emerge, and their homologies are related via the Tor-independence property. In the multigraded setting, we describe the support regions of Tor modules for quotients by sums and products of ideals generated by variables in terms of each other. |
| title | Multiple Tor modules: rigidity and Mayer-Vietoris spectral sequences |
| topic | Commutative Algebra 13D02, 18G40 (Primary), 13C12 (Secondary) |
| url | https://arxiv.org/abs/2604.20646 |