The Poincaré series of every finitely generated module over a codimension four almost complete intersection is a rational function

DOI10.1016/0022-4049(94)90062-0zbMath0812.13011OpenAlexW2019812090MaRDI QIDQ1336792

Andrew R. Kustin, Susan M. Palmer Slattery

Publication date: 8 December 1994

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(94)90062-0

zbMATH Keywords

Poincaré seriesregular local ringBetti numbersalmost complete intersection

Mathematics Subject Classification ID

Linkage, complete intersections and determinantal ideals (13C40) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Regular local rings (13H05)

Related Items (10)

Jacobian criteria for complete intersections. The graded case ⋮ Growth of Betti numbers of modules over local rings of small embedding codimension or small linkage number ⋮ Applications of Differential Graded Algebra Techniques in Commutative Algebra ⋮ Complete intersection dimension ⋮ Persistence of homology over commutative Noetherian rings ⋮ Extremal growth of Betti numbers and trivial vanishing of (co)homology ⋮ A computer-aided study of the graded Lie algebra of a local commutative noetherian ring. -- Appendix A: Some technical details about how the computer was used. -- Appendix B (by Clas Löfwall): The Lie algebra structure of a ring satisfying \({\mathcal M}_ 3\) and variants ⋮ The absolutely Koszul property of Veronese subrings and Segre products ⋮ Absolutely Koszul algebras and the Backelin-Roos property ⋮ Local rings over which all modules have rational Poincaré series

Cites Work

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• Homological Algebra on a Complete Intersection, with an Application to Group Representations
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• Tate resolutions for commutative graded algebras over a local ring

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