Results 21 to 30 of about 499 (187)
Communications in Algebra, 2016 Let $R$ be a Gorenstein local ring, $\frak{a}$ an ideal in $R$, and $M$ an $R$-module. The local cohomology of $M$ supported at $\frak{a}$ can be computed by applying the $\frak{a}$-torsion functor to an injective resolution of $M$. Since $R$ is Gorenstein, $M$ has a complete injective resolution, so it is natural to ask what one gets by applying the $\
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Extended Local Cohomology and Local Homology [PDF]
Algebras and Representation Theory, 2016 We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat R^{\mathfrak a}$ of a commutative noetherian ring $R$ with respect to a proper ideal $\mathfrak a$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat R ...
Sather-Wagstaff, Sean, Wicklein, Richard
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Vertex algebra of extended operators in 4d N=2 superconformal field theories. Part I
Journal of High Energy Physics, 2023 We construct a class of extended operators in the cohomology of a pair of twisted Schur supercharges of 4d N $$ \mathcal{N} $$ =2 SCFTs. The extended operators are constructed from the local operators in this cohomology — the Schur operators — by a ...
Philip C. Argyres +2 more
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Journal of Algebra, 1998 Let \(A\) be a commutative ring, \(M\) and \(A\)-module, \(\widetilde M\) the associated \({\mathcal O}_{\text{Spec}(A)}\)-module and \(I\) a finitely generated ideal of \(A\). The local cohomology groups \(H^n\) with respect to \(V(I) \subseteq \text{Spec}(A)\) are defined in the category of abelian sheaves. Using a generating set for \(I\) the author
Adolphson, Alan, Sperber, Steven
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UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES [PDF]
Journal of Algebraic Systems, 2013 Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module.
Moharram Aghapournahr
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Extension Functors of Generalized Local Cohomology Modules
پژوهشهای ریاضی, 2021 Introduction Throughout this paper, is a commutative Noetherian ring with non-zero identity, is an ideal of , is a finitely generated -module, and is an arbitrary -module which is not necessarily finitely generated.
Alireza Vahidi +2 more
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The Support of Local Cohomology Modules [PDF]
International Mathematics Research Notices, 2017 We describe the support of $F$-finite $F$-modules over polynomial rings $R$ of prime characteristic. Our description yields an algorithm to compute the support of such modules; the complexity of our algorithm is also analyzed. To the best of our knowledge, this is the first algorithm to avoid extensive use of Gröbner bases and hence of substantial ...
Katzman, M., Zhang, W.
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Co-Cohen-Macaulay Modules and Local Cohomology
Journal of Mathematics, 2013 Let be a commutative Noetherian local ring and let be a finitely generated -module of dimension . Then the following statements hold: (a) if width for all with , then is co-Cohen-Macaulay of Noetherian dimension ; (b) if is an unmixed -module and ...
Hero Saremi, Amir Mafi
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Socle finiteness of the local cohomology
Rocky Mountain Journal of Mathematics, 2011 Let \(R\) be a commutative local noetherian ring. Finiteness properties of local cohomology modules over \(R\) are among the basic topics of local cohomology theory. One of the main question is as follows ``Let \(I\) be an ideal of \(R\). Is the socle of \(H^n_I(R)\) finitely generated?'' A positive answer to this question for all regular local ring ...
Trlifaj, Jan, Kosan, M. Tamer
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On the cohomological dimension of the localization functor [PDF]
Proceedings of the American Mathematical Society, 1990 The localization functor of the title is defined by \(\Delta_{\lambda}(V)={\mathcal D}_{\lambda}\otimes_{{\mathcal U}_{\lambda}}V\), where \(\lambda\) is an element of the dual of a fixed Cartan subalgebra of a complex semisimple Lie algebra \({\mathfrak g}\), \({\mathcal U}_{\lambda}\) the quotient of the enveloping algebra of \({\mathfrak g}\) by the
Hecht, Henryk, Miličić, Dragan
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