Rank two filtered $(\varphi ,N)$-modules with Galois descent data and coefficients

Abstract

Let K be any finite extension of Q p , L any finite Galois extension of K, and E any finite large enough coefficient field containing L. We classify two-dimensional L-semistable E-representations of G K by listing the isomorphism classes of rank two weakly admissible filtered (ϕ, N, L/K, E)-modules.