JOURNAL ARTICLE

On Liftings of Modules of Finite Projective Dimension.

  • Published In: IMRN: International Mathematics Research Notices, 2024, v. 2024, n. 24. P. 14729 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: KC, Nawaj; Levins, Andrew J Soto 3 of 3

Abstract

The article focuses on the introduction and study of Serre liftable modules, defined as modules over a local ring that admit lifts to modules of maximal possible dimension over a regular local ring. It establishes new cases of Serre's positivity conjecture for ramified regular local rings by proving positivity for Serre liftable modules and shows that the length of such modules is bounded below by the Hilbert–Samuel multiplicity of the ring, addressing special cases of the Length Conjecture of Iyengar–Ma–Walker. The work includes examples of modules that are Serre liftable but not liftable in the classical sense, as well as modules that are not Serre liftable, and discusses implications for intersection multiplicities and homological conjectures in commutative algebra.

Additional Information

  • Source:IMRN: International Mathematics Research Notices. 2024/12, Vol. 2024, Issue 24, p14729
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:1073-7928
  • DOI:10.1093/imrn/rnae257
  • Accession Number:181969680
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