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TOPOLOGY ON COHOMOLOGY OF LOCAL FIELDS [PDF]

Forum of Mathematics, Sigma, 2015
Arithmetic duality theorems over a local field $k$ are delicate to prove if $\text{char}\,k>0$. In this case, the proofs often exploit topologies carried by the cohomology groups $H^{n}(k,G)$ for commutative finite type $k$-group schemes $G$. These ‘Čech
KĘSTUTIS ČESNAVIČIUS
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ON THE COMINIMAXNESS OF LOCAL COHOMOLOGY MODULES [PDF]

Journal of Algebraic Systems
Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules Hi I (M) are I-cominimax, for all finitely generated R-modules M and all i ∈ N0, if the R-modules Hi I (R) are I-cofinite with dimension not exceeding 1, for all ...
Ghader Ghasemi, Jafar Azami
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ON THE FINITENESS OF FORMAL LOCAL COHOMOLOGY MODULES [PDF]

Journal of Algebraic Systems, 2023
Let a be an ideal of local ring (R;m) and M a nitely generated R-module. Inthis paper, we prove some results concerning niteness and minimaxness of formal local cohomologymodules.
Shahram Rezaei, Mahbobeh Gasemi-Kalemasihi   +1 more
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GENERALIZED FORMAL LOCAL COHOMOLOGY MODULES [PDF]

Journal of Algebraic Systems, 2023
Let $a$ be an ideal of a local ring $(R, m)$ and $M$ and  $N$ two finitely generated    $R$-modules. In this paper, we introduce the concept of generalized formal local cohomology modules. We define $i$-th generalized formal local cohomology module of $M$
Shahram Rezaei, Fatemeh Lashkari
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On the Properties of Formal Local Cohomology Modules [PDF]

Journal of Mahani Mathematical Research, 2023
Let  $(R,m)$ be a commutative Noetherian local ring, $a$ an ideal of $R$. Let $t\in\Bbb N_0$ be an integer and $M$ a finitely generated $R$-module such that the $R$-module $\mathfrak{F}^i_{\mathfrak{a}}(M)$ is $\mathfrak{a}$-cominimax for all ...
Behruz Sadeqi
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TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES [PDF]

Journal of Algebraic Systems, 2021
Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then ...
A. R. Nazari, F. Rastgoo
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Local Cohomology—An Invitation [PDF]

, 2021
This article is part introduction and part survey to the mathematical area centered around local cohomology.
Walther, Uli, Zhang, Wenliang
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SERRE SUBCATEGORY, LOCAL HOMOLOGY AND LOCAL COHOMOLOGY [PDF]

Journal of Algebraic Systems, 2020
We show some results about local homology modules and local cohomology modules concerning to being in a serre sub category of the category of R-modules. Also for an ideal I of R we define the concept of CI condition on a serre category, which seems dual ...
S. O. Faramarzi, Z. Barghsouz
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ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X] [PDF]

Journal of Algebraic Systems, 2020
Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]).
M. Seidali Samani, K. Bahmanpour
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Overconvergent modular forms are highest-weight vectors in the Hodge-Tate weight zero part of completed cohomology

Forum of Mathematics, Sigma, 2021
We construct a $(\mathfrak {gl}_2, B(\mathbb {Q}_p))$ and Hecke-equivariant cup product pairing between overconvergent modular forms and the local cohomology at $0$ of a sheaf on $\mathbb {P}^1$, landing in the compactly supported completed $\mathbb {C ...
Sean Howe
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