On asymptotic socle degrees of local cohomology modules

Abstract

Let $R$ be a standard graded algebra over a field $k$ and $I$ be a homogeneous ideal of $R$. We study the question whether there is a constant $c$ such that $\Soc(H^{j}_{\fm}(R/I^t))_{<-ct}=0$ for all $t\ge 1$ and a variation of this question. We also draw a connection between this question and the notion of gauge-boundedness in prime characteristic.

Minor changes to improve exposition. Comments welcome!

References in corpus (1)

• Weak Akizuki-Nakano vanishing theorem for globally $F$-split 3-folds