Relations between Poincar\'e series for quasi-complete intersection homomorphisms
| Autor: | Pollitz, Josh, Sega, Liana M. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this article we study base change of Poincar\'e series along a quasi-complete intersection homomorphism $\varphi\colon Q \to R$, where $Q$ is a local ring with maximal ideal $\mathfrak{m}$. In particular, we give a precise relationship between the Poincar\'e series $\mathrm{P}^Q_M(t)$ of a finitely generated $R$-module $M$ to $\mathrm{P}^R_M(t)$ when the kernel of $\varphi$ is contained in $\mathfrak{m}\,\mathrm{ann}_Q(M)$. This generalizes a classical result of Shamash for complete intersection homomorphisms. Our proof goes through base change formulas for Poincar\'e series under the map of dg algebras $Q\to E$, with $E$ the Koszul complex on a minimal set of generators for the kernel of $\varphi.$ Comment: 14 pages; significant changes to Section 3, minor changes to the rest of the article. To appear in PAMS |
| Databáze: | arXiv |
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