We give bounds for various homological invariants (including Castelnuovo–Mumford regularity, degrees of local cohomology, and injective dimension) of finitely generated VI-modules in the nondescribing characteristic case. It turns out that the formulas of these bounds for VI-modules are the same as the formulas of corresponding bounds for FI-modules.
"Bounds on Homological Invariants of VI-Modules." Michigan Math. J. 69 (2) 273 - 284, May 2020. https://doi.org/10.1307/mmj/1574326878