Higher order Euler-like methods.
Let be a -adic local field with residue field such that and be a -adic representation of . Then, by using the theory of -adic differential modules, we show that is a Hodge-Tate (resp. de Rham) representation of if and only if is a Hodge-Tate (resp. de Rham) representation of where is a certain -adic local field with residue field the smallest perfect field containing .