Two obstacles exist when trying to compute K-theory of schemes: lack of $\mathbb{A}^1$-invariance and lack of a Kunneth formula. The overall goal of this project is to describe the K-theory of the affine spaces over a scheme over $\mathbb{Z}_p$ in terms of the K-theory of the scheme itself and information controlled by ``Hochschild-type" information. I aim to explain the approach of Cortinas-Haesemeyer-Weibel-Walker in characteristic zero and some progress made in mixed characteristics with Martin Spers.