PreprintCC BY 4.0arXiv
Koszul cohomology of Čech cohomology modules
Abstract
Let R be a commutative Noetherian ring, let x=x1,…,xn be an R-regular sequence, and let y=y1,…,ym be a sequence of elements of R. Put I=(y). Let 𝒮 be a Serre subcategory of the category of R-modules. We consider the double complex obtained from the Koszul co-complex with respect to x and the Čech complex with respect to y. Using the two spectral sequences associated with this double complex, we prove that ExtRi(R/(x),HIj(R))∈𝒮 for all i,j∈ ℕ0 implies HIj(R/(x))∈𝒮 for all j∈ℕ0.
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BibTeX
@misc{jahangiri2026koszul,
title = {{Koszul cohomology of Čech cohomology modules}},
author = {Maryam Jahangiri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.20171},
eprint = {2608.20171},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20171},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Koszul cohomology of Čech cohomology modules
AU - Maryam Jahangiri
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2608.20171
UR - https://arxiv.org/abs/2608.20171
AB - Let R be a commutative Noetherian ring, let x=x_1,…,x_n be an R-regular sequence, and let y=y_1,…,y_m be a sequence of elements of R. Put I=(y). Let 𝒮 be a Serre subcategory of the category of R-modules. We consider the double complex obtained from the Koszul co-complex with respect to x and the Čech complex with respect to y. Using the two spectral sequences associated with this double complex, we prove that Ext_R^i(R/(x),H_I^j(R))∈𝒮 for all i,j∈ ℕ_0 implies H_I^j(R/(x))∈𝒮 for all j∈ℕ_0.
ER -