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Let $L$ be finite extension of $\mathbb{Q}_p$ with ring of integers$\mathcal{O}_L$. I show that periodic topological cyclic homology of$\mathcal{O}_L$, over the base $\mathbb{E}_{\infty}$-ring$\mathbb{S}_{W(\mathbb{F}_q)}[z]$ carries a $p$-height one formal group law mod$p$ that depends on the Eisenstein polynomial of $L$ over $\mathbb{Q}_p$ for achoice of uniformizer $\varpi\in \mathcal{O}_L$.

Complex orientations and $\text{TP}$ of complete DVRS