Sudeshna Roy
TIFR, Mumbai
February 2, 2023
Graded components of local cohomology modules supported on $\mathfrak{C}$-monomial ideals.: The structure of local cohomology modules is quite mysterious owing to their non-finite generation. Over the last three decades, researchers have extensively investigated if they behave like finitely-generated modules. Let $A$ be a Dedekind domain of characteristic zero such that its localization at every maximal ideal has mixed characteristic with finite residue field. Let $R=A[X_1, \ldots, X_n]$ be a polynomial ring equipped with the standard multigrading and let $I\subseteq R$ be a $\mathfrak{C}$-monomial ideal. We call an ideal in $R$ a $\mathfrak{C}$-monomial ideal if it can be generated by elements of the form $aU$ where $a \in A$ (possibly nonunit) and $U$ is a monomial in $X_i$'s. Local cohomology modules supported on usual monomial ideals of a polynomial ring over a field gains a great deal of interest due to its connections with combinatorics and toric varieties. The objective of this talk is to discuss a structure theorem for the multigraded components of the local cohomolo
TIFR, Mumbai
February 2, 2023
Graded components of local cohomology modules supported on $\mathfrak{C}$-monomial ideals.: The structure of local cohomology modules is quite mysterious owing to their non-finite generation. Over the last three decades, researchers have extensively investigated if they behave like finitely-generated modules. Let $A$ be a Dedekind domain of characteristic zero such that its localization at every maximal ideal has mixed characteristic with finite residue field. Let $R=A[X_1, \ldots, X_n]$ be a polynomial ring equipped with the standard multigrading and let $I\subseteq R$ be a $\mathfrak{C}$-monomial ideal. We call an ideal in $R$ a $\mathfrak{C}$-monomial ideal if it can be generated by elements of the form $aU$ where $a \in A$ (possibly nonunit) and $U$ is a monomial in $X_i$'s. Local cohomology modules supported on usual monomial ideals of a polynomial ring over a field gains a great deal of interest due to its connections with combinatorics and toric varieties. The objective of this talk is to discuss a structure theorem for the multigraded components of the local cohomolo