A note on the growth of regularity with respect to Frobenius

Abstract

Let $R=k[x_1,\dots ,x_n]/I$ be a standard graded $k$-algebra where $k$ is a field of prime characteristic and let $J$ be a homogeneous ideal in $R$. Denote $(x_1,\dots ,x_n)$ by $\mathfrak{m}$. We prove that there is a constant $C$ (independent of $e$) such that the regularity of $H_{\mathfrak{m}}^s(R/J^{[p^e]})$ is bounded above by $C{p}^e$ for all $e\ge 1$ and all integers $s$ such that $s+1$ is at least the dimension of the locus where $R/J$ doesn't have finite projective dimension.

Comments are welcome

References in corpus (1)

• On the behavior of Castelnuovo-Mumford regularity with respect to some functors

Cited by in corpus (3)

• On the existence of $F$-thresholds and related limits
• Local cohomology -- an invitation
• $F$-Invariants of Stanley-Reisner Rings