11 citations · 56 across the 19 of their papers we have counts for
19 papers
Finite homological dimension of Hom, vanishing of Ext, and applications to divisor class group
Souvik Dey, Dipankar Ghosh
For finitely generated modules and over a commutative Noetherian local ring , we give various sufficient criteria for detecting freeness of or via vanishing of…
Gorenstein rings via homological dimensions, and symmetry in vanishing of Ext and Tate cohomology
Dipankar Ghosh, Tony J. Puthenpurakal
The aim of this article is to consider the spectral sequences induced by tensor-hom adjunction, and provide a number of new results. Let be a commutative Noetherian local ring…
Homological dimensions of Burch ideals, submodules and quotients
Dipankar Ghosh, Aniruddha Saha
The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this article is…
Integrally closed -primary ideals have extremal resolutions
Dipankar Ghosh, Tony J. Puthenpurakal
We show that every integrally closed -primary ideal in a commutative Noetherian local ring has maximal complexity and curvature, i.e., $ {\rm…
Complexity and rigidity of Ulrich modules, and some applications
Souvik Dey, Dipankar Ghosh
We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can be used as test modules, which detect finite homological dimensions of modules. We prove that Ul…
Auslander-Reiten conjecture and finite injective dimension of Hom
Dipankar Ghosh, Ryo Takahashi
For a finitely generated module over a commutative Noetherian ring , we settle the Auslander-Reiten conjecture when at least one of and ${\rm Hom}_R(M,M…
The (ir)regularity of Tor and Ext
Marc Chardin, Dipankar Ghosh, Navid Nemati
We investigate the asymptotic behaviour of Castelnuovo-Mumford regularity of Ext and Tor, with respect to the homological degree, over complete intersection rings. We derive from a…
Linear resolution of products of monomial ideals related to maximal minors
Arindam Banerjee, Dipankar Ghosh, S. Selvaraja
Let be an matrix of distinct indeterminates over a field , where . Set the polynomial ring …
Gorensteinness of short local rings in terms of the vanishing of Ext and Tor
Dipankar Ghosh
Let be a commutative Noetherian local ring which contains a regular sequence su…
An asymptotic bound for Castelnuovo-Mumford regularity of certain Ext modules over graded complete intersection rings
Dipankar Ghosh, Tony J. Puthenpurakal
Set , where is a polynomial ring over a field, and is a homogeneous -regular sequence. Let and be finitely g…
Asymptotic Prime Divisors Related to Ext, Regularity of Powers of Ideals, and Syzygy Modules
Dipankar Ghosh
This dissertation focuses on the following topics: (1) asymptotic prime divisors over complete intersection rings, (2) asymptotic stability of complexities over complete intersecti…
Asymptotic associate primes
Dipankar Ghosh, Provanjan Mallick, Tony J. Puthenpurakal
We investigate three cases regarding asymptotic associate primes. First, assume is an excellent Cohen-Macaulay (CM) non-regular local ring, and $ M = \operator…
Vanishing of (co)homology over deformations of Cohen-Macaulay local rings of minimal multiplicity
Dipankar Ghosh, Tony J. Puthenpurakal
Let be a -dimensional Cohen-Macaulay (CM) local ring of minimal multiplicity. Set , where is an -regular sequence.…
Some criteria for regular and Gorenstein local rings via syzygy modules
Dipankar Ghosh
Let be a Cohen-Macaulay local ring. We prove that the th syzygy module of a maximal Cohen-Macaulay -module cannot have a semidualizing direct summand for every $ n…
A short proof of a result of Katz and West
Dipankar Ghosh, Tony J. Puthenpurakal
We give a short proof of a result due to Katz and West: Let be a Noetherian ring and ideals of . Let and be finitely generated -modules and $N' \…
Characterizations of regular local rings via syzygy modules of the residue field
Dipankar Ghosh, Anjan Gupta, Tony J. Puthenpurakal
Let be a commutative Noetherian local ring with residue field . We show that if a finite direct sum of syzygy modules of surjects onto `a semidualizing module' or `a non…
Existence of special primary decompositions in multigraded modules
Dipankar Ghosh
Let be a commutative Noetherian -graded ring, and $L = \bigoplus_{\underline{n}\in\mathbb{N}^t}L_{\und…
Asymptotic linear bounds of Castelnuovo-Mumford regularity in multigraded modules
Dipankar Ghosh
Let be a Noetherian standard -graded algebra over an Artinian local ring . Let be homogeneous ideals of and a finitely generated $\mat…
Asymptotic prime divisors over complete intersection rings
Dipankar Ghosh, Tony J. Puthenpurakal
Let be a local complete intersection ring. Let be two finitely generated -modules and an ideal of . We prove that \[ \bigcup_{i\geqslant 0}\bigcup_{n \geqslant…