Local cohomology, cofiniteness and homological functors of modules

Kamal Bahmanpour

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 2, page 541-558
  • ISSN: 0011-4642

Abstract

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Let I be an ideal of a commutative Noetherian ring R . It is shown that the R -modules H I j ( M ) are I -cofinite for all finitely generated R -modules M and all j ∈ ℕ 0 if and only if the R -modules Ext R i ( N , H I j ( M ) ) and Tor i R ( N , H I j ( M ) ) are I -cofinite for all finitely generated R -modules M , N and all integers i , j ∈ ℕ 0 .

How to cite

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Bahmanpour, Kamal. "Local cohomology, cofiniteness and homological functors of modules." Czechoslovak Mathematical Journal 72.2 (2022): 541-558. <http://eudml.org/doc/298309>.

@article{Bahmanpour2022,
abstract = {Let $I$ be an ideal of a commutative Noetherian ring $R$. It is shown that the $R$-modules $H^j_I(M)$ are $I$-cofinite for all finitely generated $R$-modules $M$ and all $j\in \mathbb \{N\}_0$ if and only if the $R$-modules $\{\rm Ext\}^i_R(N,H^j_I(M))$ and $\{\rm Tor\}^R_i(N,H^j_I(M))$ are $I$-cofinite for all finitely generated $R$-modules $M$, $N$ and all integers $i,j\in \mathbb \{N\}_0$.},
author = {Bahmanpour, Kamal},
journal = {Czechoslovak Mathematical Journal},
keywords = {cofinite module; cohomological dimension; ideal transform; local cohomology; Noetherian ring},
language = {eng},
number = {2},
pages = {541-558},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Local cohomology, cofiniteness and homological functors of modules},
url = {http://eudml.org/doc/298309},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Bahmanpour, Kamal
TI - Local cohomology, cofiniteness and homological functors of modules
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 2
SP - 541
EP - 558
AB - Let $I$ be an ideal of a commutative Noetherian ring $R$. It is shown that the $R$-modules $H^j_I(M)$ are $I$-cofinite for all finitely generated $R$-modules $M$ and all $j\in \mathbb {N}_0$ if and only if the $R$-modules ${\rm Ext}^i_R(N,H^j_I(M))$ and ${\rm Tor}^R_i(N,H^j_I(M))$ are $I$-cofinite for all finitely generated $R$-modules $M$, $N$ and all integers $i,j\in \mathbb {N}_0$.
LA - eng
KW - cofinite module; cohomological dimension; ideal transform; local cohomology; Noetherian ring
UR - http://eudml.org/doc/298309
ER -

References

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