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Restricting Homology to Hypersurfaces

  • Luchezar L. Avramov
  • Srikanth B. IyengarEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)

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.

Keywords

Elementary abelian group Complete intersection Rank variety Support set 

2010 Mathematics Subject Classification

13D07 (primary) 16E45 13D02 13D40 (secondary) 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of NebraskaLincolnU.S.A.
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityU.S.A.

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