Abstract
This paper concerns the homological properties of a module M over a ring R relative to a presentation \(R\cong P/I\), where P is local ring. It is proved that the Betti sequence of M with respect to P / (f) for a regular element f in I depends only on the class of f in \(I/\mathfrak {n} I\), where \(\mathfrak {n}\) is the maximal ideal of P. Applications to the theory of supports sets in local algebra and in the modular representation theory of elementary abelian groups are presented.
To Dave Benson on the occasion of his 60th birthday
Partly supported by NSF grants DMS-1103176 (LLA) and DMS-1700985 (SBI). We are grateful to Chris Drupieski for comments on earlier version of this manuscript.
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Avramov, L.L., Iyengar, S.B. (2018). Restricting Homology to Hypersurfaces. In: Carlson, J., Iyengar, S., Pevtsova, J. (eds) Geometric and Topological Aspects of the Representation Theory of Finite Groups. PSSW 2016. Springer Proceedings in Mathematics & Statistics, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-319-94033-5_1
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DOI: https://doi.org/10.1007/978-3-319-94033-5_1
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