Sayed Sadiqul Islam

activity

20242026

collaborators

6 papers

math.AC2026

On the structure theorem of graded components of $F$ -finite, $F$ -modules over certain polynomial ring

Sayed Sadiqul Islam

Let $K$ be a field of characteristic $p > 0$ , $A = K [[Y]]$ be a power series ring in one variable and $Q (A)$ be the field of fraction of $A$ . Suppose that $R = A [X_{1}, \dots, X_{n}]$ is a st…

math.AC2026

On Bass numbers of graded components of local cohomology modules supported on $C$ -monomial ideals in mixed characteristic

Sayed Sadiqul Islam, Tony J. Puthenpurakal

Let $A$ be a Dedekind domain of characteristic zero such that for each height one prime ideal $p$ in $A$ , the local ring $A_{p}$ has mixed characteristic with…

math.AC2025

Local cohomology modules of a regular affine domain

Sayed Sadiqul Islam

For a Noetherian commutative ring $R$ , let $H_{I}^{i} (R)$ be the $i$ -th local cohomology module of $R$ with respect to $I$ . In \cite{Hel-08}, Hellus posed the question of identifying…

math.AC2025

Bounds on Bass numbers of local cohomology modules

Sayed Sadiqul Islam, Tony J. Puthenpurakal

Let $R = K [x_{1}, \dots, x_{m}]$ where $K$ is an uncountable algebraically closed field of characteristic $0$ . For a prime ideal $P$ of $R$ , let $μ_{j} (P, M)$ be the $j$ -th Bass number of an…

math.AC2025

Bigraded components of F-finite F-modules

Sayed Sadiqul Islam, Tony J. Puthenpurakal

Let $A$ be a regular ring containing a field of characteristic $p > 0$ and let $R = A [x_{1}, \dots, x_{m}, y_{1}, \dots, y_{n}]$ be standard bigraded over $A$ , i.e., $\operatorname{bideg}(A)=(0,0…

math.AC2024

On some Rings of differentiable type

Sayed Sadiqul Islam, Tony J. Puthenpurakal

Let $K$ be a field of characteristic 0 and $S = K [x_{1}, \dots, x_{m}] / I$ be an affine domain. Consider $R = S_{P}$ where $P \in S p ec (S)$ such that $R$ is regular. In this paper we construct a…

On the structure theorem of graded components of F-finite, F-modules over certain polynomial ring

On Bass numbers of graded components of local cohomology modules supported on C-monomial ideals in mixed characteristic

Local cohomology modules of a regular affine domain

Bounds on Bass numbers of local cohomology modules

Bigraded components of F-finite F-modules

On some Rings of differentiable type

On the structure theorem of graded components of $F$ -finite, $F$ -modules over certain polynomial ring

On Bass numbers of graded components of local cohomology modules supported on $C$ -monomial ideals in mixed characteristic