A noncommutative analogue of the Peskine--Szpiro Acyclicity Lemma
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866917851474952192 |
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| author | Bath, Daniel |
| author_facet | Bath, Daniel |
| contents | We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular rings. In the case of relative $\mathscr{D}_{X}$-modules, for example $\mathscr{D}_{X}[s_{1}, \dots, s_{r}]$-modules, the hypotheses have geometric realizations making them easier to authenticate. We demonstrate the efficacy of this lemma and its various forms by: independently recovering some results related to Bernstein--Sato polynomials; establishing a new result about quasi-free structures of free multi-derivations of hyperplane arrangements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_14223 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A noncommutative analogue of the Peskine--Szpiro Acyclicity Lemma Bath, Daniel Algebraic Geometry 14F10, 13D02, 13C15, 13N10, 16E05, 32C38, 32S65, 32S40 We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular rings. In the case of relative $\mathscr{D}_{X}$-modules, for example $\mathscr{D}_{X}[s_{1}, \dots, s_{r}]$-modules, the hypotheses have geometric realizations making them easier to authenticate. We demonstrate the efficacy of this lemma and its various forms by: independently recovering some results related to Bernstein--Sato polynomials; establishing a new result about quasi-free structures of free multi-derivations of hyperplane arrangements. |
| title | A noncommutative analogue of the Peskine--Szpiro Acyclicity Lemma |
| topic | Algebraic Geometry 14F10, 13D02, 13C15, 13N10, 16E05, 32C38, 32S65, 32S40 |
| url | https://arxiv.org/abs/2109.14223 |