A representative of RΓ(N,T) for higher dimensional twists of ℤpr(1)

Let [Formula: see text] be a Galois extension of text]-adic number fields and let de Rham representation the absolute group text]. In case text], equivariant local text]-constant conjecture describes compatibility Tamagawa with functional equation Artin text]-functions it can formulated as vanishing certain element in text]; similar approach followed also unramified twists (see [W. Bley A. Cobbe, The for Acta Arith. 178(4) (2017) 313–383; D. Izychev O. Venjakob, Equivariant epsilon 1-dimensional Lubin–Tate groups, J. Théor. Nr. Bordx. 28(2) (2016) 485–521]). One main technical difficulties computation arises from so-called cohomological term which requires construction bounded complex cohomologically trivial modules represents full text]-stable text]-sublattice this paper, we generalize Theorem 2 313–383] to higher dimensional