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Acta Mathematica Vietnamica

, Volume 42, Issue 1, pp 37–60 | Cite as

Local Cohomology Annihilators and Macaulayfication

  • Nguyen Tu Cuong
  • Doan Trung CuongEmail author
Article

Abstract

The aim of this paper is to study a deep connection between local cohomology annihilators and Macaulayfication and arithmetic Macaulayfication over a local ring. Local cohomology annihilators appear through the notion of p-standard system of parameters. For a local ring, we prove an equivalence of the existence of Macaulayfications, the existence of a p-standard system of parameters, being a quotient of a Cohen-Macaulay local ring, and the verification of Faltings’ Annihilator theorem. For a finitely generated module which is unmixed and faithful, we prove an equivalence of the existence of an arithmetic Macaulayfication and the existence of a p-standard system of parameters; and both are proved to be equivalent to the existence of an arithmetic Macaulayfication on the ground ring. A connection between Macaulayfication and universal catenaricity is also discussed.

Keywords

Arithmetic Macaulayfication Macaulayfication Local cohomology annihilator P-standard system of parameters Quotient of Cohen-Macaulay ring 

Mathematics Subject Classification (2010)

Primary 13H10 14M05 Secondary 13D45 14B05 

Notes

Acknowledgments

The authors thank M. Brodmann and S. Goto for useful discussions and comments during this work. They thank the anonymous referee for some helpful comments on the earlier version. The second author thanks the Vietnam Institute for Advanced Study in Mathematics (VIASM), Vietnam, and the Institute for Mathematical Sciences (IMS-NUS), Singapore, for the support and hospitality during his visit to these institutions.

Nguyen Tu Cuong is supported by the NAFOSTED of Vietnam under grant number 101.04-2014.25.

Doan Trung Cuong is partially supported by the SFB/TR 45 “Periods, moduli spaces and arithmetic of algebraic varieties” and by the NAFOSTED of Vietnam.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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