On Projective and Flat Persistence Modules
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910039120281600 |
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| author | Chakraborty, Prateep Ghosh, Giriraj |
| author_facet | Chakraborty, Prateep Ghosh, Giriraj |
| contents | In recent years, persistence modules have been viewed as graded modules with gradation over a preordered set serving as the indexing set. We provide sufficient criteria for a projective module over a PID to be free when the indexing set is a lattice. With a lattice as the indexing set, we obtain criteria ensuring that a given persistence module is not projective. When the indexing set is a preordered set, we establish the flatness of a well-known family of persistence modules. We end the article with two algorithms to compute a basis of free persistence modules with indexing sets $\mathbb{Z}$ and $\mathbb{Z}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02674 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Projective and Flat Persistence Modules Chakraborty, Prateep Ghosh, Giriraj Algebraic Topology 55N31, 13C10, 13C11 (Primary), 06A07, 06A11 (Secondary) In recent years, persistence modules have been viewed as graded modules with gradation over a preordered set serving as the indexing set. We provide sufficient criteria for a projective module over a PID to be free when the indexing set is a lattice. With a lattice as the indexing set, we obtain criteria ensuring that a given persistence module is not projective. When the indexing set is a preordered set, we establish the flatness of a well-known family of persistence modules. We end the article with two algorithms to compute a basis of free persistence modules with indexing sets $\mathbb{Z}$ and $\mathbb{Z}^2$. |
| title | On Projective and Flat Persistence Modules |
| topic | Algebraic Topology 55N31, 13C10, 13C11 (Primary), 06A07, 06A11 (Secondary) |
| url | https://arxiv.org/abs/2603.02674 |