Lyubeznik numbers, $F$-modules and modules of generalized fractions

Mordechai Katzman; Rodney Y. Sharp

Lyubeznik numbers, $F$-modules and modules of generalized fractions

Commutative Algebra 2022-04-06 v2

Authors: Mordechai Katzman , Rodney Y. Sharp

Abstract

This paper presents an algorithm for calculation of the Lyubeznik numbers of a local ring which is a homomorphic image of a regular local ring $R$ of prime characteristic. The methods used employ Lyubeznik's $F$ -modules over $R$ , particularly his $F$ -finite $F$ -modules, and also the modules of generalized fractions of Sharp and Zakeri. It is shown that many modules of generalized fractions over $R$ have natural structures as $F$ -modules; these lead to $F$ -module structures on certain local cohomology modules over $R$ , which are exploited, in conjunction with $F$ -module structures on injective $R$ -modules that result from work of Huneke and Sharp, to compute Lyubeznik numbers. The resulting algorithm has been implemented in Macaulay2.

Keywords

Lyubeznik numbers $F$-modules modules of generalized fractions local cohomology regular local ring Macaulay2 prime characteristic

Cite

@article{arxiv.2006.05438,
  title  = {Lyubeznik numbers, $F$-modules and modules of generalized fractions},
  author = {Mordechai Katzman and Rodney Y. Sharp},
  journal= {arXiv preprint arXiv:2006.05438},
  year   = {2022}
}

Comments

Comments appreciated! To appear in the Transactions of the AMS

Lyubeznik numbers, $F$-modules and modules of generalized fractions

Abstract

Keywords

Cite

Comments

Related papers