Mod $p$ Buchstaber Invariant

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