Relations between Poincaré series for quasi-complete intersection homomorphisms

2024/03/25 by Josh Pollitz, Pollitz, Josh, Liana M. Şega +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2403.17079

Abstract

In this article we study base change of Poincaré series along a quasi-complete intersection homomorphism φ\colon Q → R, where Q is a local ring with maximal ideal \mathfrakm. In particular, we give a precise relationship between the Poincaré series P^Q_M(t) of a finitely generated R-module M to P^R_M(t) when the kernel of φ is contained in \mathfrakm ann_Q(M). This generalizes a classical result of Shamash for complete intersection homomorphisms. Our proof goes through base change formulas for Poincaré series under the map of dg algebras Q→ E, with E the Koszul complex on a minimal set of generators for the kernel of φ.

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