The equivariant local epsilon-constant conjecture for potentially semistable representations

Let $K$ be a finite extension of ${\mathbb Q}_p$, let $N/K$ be a finite Galois extension with Galois group $G$, and let $T$ be a ${\mathbb Z}_p[G_K]$-lattice such that $V={\mathbb Q}_p\otimes_{{\mathbb Z}_p}T$ is potentially semistable. The notation $\Delta_{EP}^{na}(N/K,T)$, $\delta(N/K,V)$, $\tilde\Lambda$, and $\tilde\Omega$ denotes the canonical element and trivialization introduced above and the corresponding coefficient rings. Equivariant local epsilon-constant conjecture. The class

[(\Delta_{EP}^{na}(N/K,T),\delta(N/K,V))]\in\pi_0(V({\mathbb Z}_p[G]},\tilde\Omega))

is trivial in

$$\pi_0(V(\tilde\Lambda,\tilde\Omega)).$$

This is the central equivariant local epsilon-constant assertion, generalizing the conjectures of Izychev–Venjakob and Breuning; its resolution is not supplied in the given text.