Onset of regularity for \textbf{FI}-modules (Q6151731)

\textit{W. L. Gan} [New York J. Math. 22, 1487--1502 (2016; Zbl 1358.18006), Theorem 21] and \textit{R. Nagpal} et al. [Proc. Am. Math. Soc. 146, No. 10, 4117--4126 (2018; Zbl 1408.13048), Theorem 1], concerned with homological aspects of \(\boldsymbol{FI}\)-modules, established a result reminiscent of the relationship between the syzgyies and the local cohomology of a graded module over a polynomial ring in commutative algebra [\textit{D. Eisenbud} and \textit{S. Goto}, J. Algebra 88, 89--133 (1984; Zbl 0531.13015)]. This paper establishes an explicit range for the stabilization of the weakly increasing sequence in the above theorem in terms of local cohomology.