Mod $p$ Buchstaber invariant

We investigate the mod $p$ Buchstaber invariant of the skeleta of simplices, for a prime number $p$, and compare them for different values of $p$. For $p=2$, the invariant is the real Buchstaber invariant. Our findings reveal that these values are generally distinct. Additionally, we determine or estimate the mod $p$ Buchstaber invariants of certain universal simplicial complexes $X({\text{F}}_p^n)$.