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

Abstract

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 a choice of uniformizer $\varpi \in {\mathcal{O}}_L$.

arXiv comment9 pages, including references. Accepted version