Abstract: Stanley-Reisner rings are a class of combinatorial rings associated to simplicial complexes. These rings are typically defined as algebras over a field, and in this setting there are many well-known connections between the algebraic properties of the ring and the topological properties of the associated simplicial complex. In this talk, we will discuss the analogous class of "$t$-Stanley-Reisner" rings in mixed characteristic. We adapt classical theorems from Stanley-Reisner theory—in particular, Hochster's formula for Betti numbers and Terai's theorem on Serre conditions. As a case study, we examine the $t$-Stanley-Reisner ring defined by a triangulation of the real projective plane $\mathbb{P}^2_{\mathbb{R}}$. This example will highlight the unique behavior that distinguishes $t$-Stanley-Reisner rings from their equal characteristic cousins.