Modules of finite injective dimension
M Asgharzadeh - arXiv preprint arXiv:2301.01105, 2023 - arxiv.org
We study some aspects of distinguished finitely generated modules of finite injective
dimension. Following Bass' conjecture, this implies that the ring is Cohen-Macaulay. We …
dimension. Following Bass' conjecture, this implies that the ring is Cohen-Macaulay. We …
A note on cohomological vanishing theorems
M Asgharzadeh - arXiv preprint arXiv:2401.14133, 2024 - arxiv.org
We study $ cd (M, N):=\sup\{j: H^ j_ {m}(M, N)\neq0\} $, and we prove the following over $ AB
$-rings: $ cd (M, N)<\infty $ iff $ cd (M, N)\leq2 dim R $. For locally free over the punctured …
$-rings: $ cd (M, N)<\infty $ iff $ cd (M, N)\leq2 dim R $. For locally free over the punctured …
A note on $ UFD$
M Asgharzadeh - arXiv preprint arXiv:2308.14465, 2023 - arxiv.org
We search for principal ideals. As a sample, let $ R $ be a strongly-normal, almost-factorial,
and complete-intersection local ring with a prime ideal $ P $ of height one. If $ depth …
and complete-intersection local ring with a prime ideal $ P $ of height one. If $ depth …
Some results on vanishing of Ext and finite Gorenstein dimension of the dual of a module
VD Mendoza-Rubio, VH Jorge-Pérez - arXiv preprint arXiv:2312.06124, 2023 - arxiv.org
arXiv:2312.06124v1 [math.AC] 11 Dec 2023 Page 1 arXiv:2312.06124v1 [math.AC] 11 Dec
2023 SOME RESULTS ON VANISHING OF EXT AND FINITE GORENSTEIN DIMENSION OF …
2023 SOME RESULTS ON VANISHING OF EXT AND FINITE GORENSTEIN DIMENSION OF …
Cohomological splitting, realization, and finiteness
M Asgharzadeh - arXiv preprint arXiv:2101.08187, 2021 - arxiv.org
We search for some splitting (resp. finiteness) criteria of a given module $ M $ over a local
ring $(R,\fm, k) $ in terms of the splitting (resp. finiteness) property of certain cohomological …
ring $(R,\fm, k) $ in terms of the splitting (resp. finiteness) property of certain cohomological …
Grothendieck-Lefschetz for vector bundles
K Cesnavicius - arXiv preprint arXiv:1802.08203, 2018 - arxiv.org
According to the Grothendieck-Lefschetz theorem from SGA 2, there are no nontrivial line
bundles on the punctured spectrum $ U_R $ of a local ring $ R $ that is a complete …
bundles on the punctured spectrum $ U_R $ of a local ring $ R $ that is a complete …
A note on the homology of differentials
M Asgharzadeh - arXiv preprint arXiv:2012.11427, 2020 - arxiv.org
arXiv:2012.11427v2 [math.AC] 17 May 2021 Page 1 arXiv:2012.11427v2 [math.AC] 17 May
2021 A NOTE ON THE HOMOLOGY OF DIFFERENTIALS MOHSEN ASGHARZADEH …
2021 A NOTE ON THE HOMOLOGY OF DIFFERENTIALS MOHSEN ASGHARZADEH …