  Let K be a complete discrete valuation field of mixed characteristic (0,p)
and G_K the absolute Galois group of K. In this paper, we will prove the p-adic
monodromy theorem for p-adic representations of G_K without any assumption on
the residue field of K, for example the finiteness of a p-basis of the residue
field of K. The main point of the proof is a construction of (phi,G_K)-module
Nrig^+(V) for a de Rham representation V, which is a generalization of Pierre
Colmez' Nrig^+(V). In particular, our proof is essentially different from
Kazuma Morita's proof in the case when the residue field admits a finite
p-basis.
  We also give a few applications of the p-adic monodromy theorem, which are
not mentioned in the literature. First, we prove a horizontal analogue of the
p-adic monodromy theorem. Secondly, we prove an equivalence of categories
between the category of horizontal de Rham representations of G_K and the
category of de Rham representations of an absolute Galois group of the
canonical subfield of K. Finally, we compute H^1 of some p-adic representations
of G_K, which is a generalization of Osamu Hyodo's results.
