Virtual Specht stability for FI-modules in positive characteristic

We define a notion of virtual Specht stability which is a relaxation of the Church-Farb notion of representation stability for sequences of symmetric group representations. Using a structural result of Nagpal, we show that FI-modules over fields of positive characteristic exhibit virtual Specht stability. As a corollary we answer a question posed by Farb in his 2014 ICM address.