In this paper we formulate a conjecture on the relationship between the equivariant ǫ-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 Zp-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 Zp by extending the ideas of [Breu] from the case of the multiplicative group Gm to arbitrary one-dimensional Lubin-Tate groups. For the connection to the different formulations of the ǫ-conjecture in [BB], [FK], [Breu], [BlB] and [BF] see [Iz].
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