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Finiteness of local cohomology modules over arbitrary regular local rings
Abstract
In this paper, we consider arbitrary regular local ring S and an ideal J⊂ S whose minimal primes are cohomologically complete intersection. Using the Mayer-Vietoris spectral sequence, in Section 2, we construct examples of local cohomology modules HiJ (S), whose set of associated primes is finite. As a special case we show that the set of associated primes HiJ (S) is finite when minimal primes of J are part of a specific regular system of parameters and satisfy a `Dropping Condition'. In Section 3, we prove Theorem 2.3 along with its asssociated corollary in a more general setting, without the use of `Dropping Condition'. These examples of local cohomology modules include the cases whose associative primes also can contain prime number p.
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BibTeX
@misc{bhattacharyya2026finiteness,
title = {{Finiteness of local cohomology modules over arbitrary regular local rings}},
author = {Rajsekhar Bhattacharyya},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.10064},
eprint = {2611.10064},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.10064},
}
RIS
TY - UNPB
TI - Finiteness of local cohomology modules over arbitrary regular local rings
AU - Rajsekhar Bhattacharyya
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2611.10064
UR - https://arxiv.org/abs/2611.10064
AB - In this paper, we consider arbitrary regular local ring S and an ideal J⊂ S whose minimal primes are cohomologically complete intersection. Using the Mayer-Vietoris spectral sequence, in Section 2, we construct examples of local cohomology modules H^i_J (S), whose set of associated primes is finite. As a special case we show that the set of associated primes H^i_J (S) is finite when minimal primes of J are part of a specific regular system of parameters and satisfy a `Dropping Condition'. In Section 3, we prove Theorem 2.3 along with its asssociated corollary in a more general setting, without the use of `Dropping Condition'. These examples of local cohomology modules include the cases whose associative primes also can contain prime number p.
ER -