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}.
Categories: math.NT