  In this paper we formulate a conjecture on the relationship between the
equivariant \epsilon-constants (associated to a local p-adic representation V
and a finite extension of local fields L/K) and local Galois cohomology groups
of a Galois stable \mathbb{Z}_{p}-lattice T of V. We prove the conjecture for
L/K being an unramified extension of degree prime to p and T being a p-adic
Tate module of a one-dimensional Lubin-Tate group defined over \mathbb{Z}_{p}
by extending the ideas of \cite{Breu} from the case of the multiplicative group
\mathbb{G}_{m} to arbitrary one-dimensional Lubin-Tate groups. For the
connection to the different formulations of the \epsilon-conjecture in
\cite{BB}, \cite{FK}, \cite{Breu}, \cite{BlB} and \cite{BF} see \cite{Iz}.
