Equivariant local Epsilon Constants and Etale Cohomology

A conjecture is formulated which relates the equivariant localepsilon constant of a Galois extension of p-adic fields to anatural algebraic invariant coming from étale cohomology.Some evidence for the conjecture is provided and its relationto a conjecture for the equivariant global epsilon constantof an extension of number fields formulated by Bley and Burnsis established.