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Behaviour of Finiteness of the Set of Associated Primes under Ring Extensions
Rajsekhar Bhattacharyya
We study the behaviour of the finiteness of the set of associated primes of local cohomology modules, more generally of Lyubeznik functors, under various ring extensions. At first,…
Examples of local Cohomology Modules for Ramified Regular Local Rings having Finite Set of Associated Primes
Rajsekhar Bhattacharyya
Lyubeznik's conjecture, (\cite{Ly1}, Remark 3.7) asserts the finiteness of the set ssociated primes of local cohomology modules for regular rings. But, in the case of ramified regu…
A Note on Associated Primes and Bockstein Homomorphisms of Local Cohomology Modules for Ramified Regular Local Rings
Rajsekhar Bhattacharyya
For a Noetherian regular ring and for a fixed ideal , assume that the associated primes of local cohomology module does not contain for some $i\geq 0…
Behaviour of the Support of Lyubeznik Functors under Ring Extensions
Rajsekhar Bhattacharyya
Let be an arbitrary ring extension of Noetherian rings. In this article we study the behaviour of Zariski closedness of the support of Lyubeznik functors $\mathrm{…
Smooth Algebra and Finiteness of the Set of Associated Primes of Local Cohomology Modules
Rajsekhar Bhattacharyya
In this article, we study the behaviour of smooth algebra over local Noetherian local ring . At first, we observe that for every , has finite length in the cat…