English

Bass Numbers of the First Nonzero Local Cohomology Module

Commutative Algebra 2024-02-27 v1

Abstract

Let RR be a regular local ring containing a field, let II be an ideal with d=htId=\text{ht}{I}, and assume htp=d\text{ht}{p}=d for every minimal prime pp of II. We compute the Bass numbers μ0(q,HId(R))\mu^{0}(q,H_{I}^{d}(R)) and μ1(q,HId(R))\mu^{1}(q,H_{I}^{d}(R)) for all primes qq. We then study μ2(q,HId(R))\mu^{2}(q,H_{I}^{d}(R)) by considering the associated primes of HId+1(R)H_{I}^{d+1}(R).

Keywords

Cite

@article{arxiv.2402.15667,
  title  = {Bass Numbers of the First Nonzero Local Cohomology Module},
  author = {Andrew J. Soto Levins},
  journal= {arXiv preprint arXiv:2402.15667},
  year   = {2024}
}