Sayed Sadiqul Islam

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20242026

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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…