  This book presents two important results in p-adic Hodge theory following the
approach initiated by Faltings, namely (i) his main p-adic comparison theorem,
and (ii) the Hodge-Tate spectral sequence. We establish for each of these
results two versions, an absolute one and a relative one. While the absolute
statements can reasonably be considered as well understood, particularly after
their extension to rigid varieties by Scholze, Faltings' initial approach for
the relative variants has remained much less studied. Although we follow the
same strategy as that used by Faltings to establish his main p-adic comparison
theorem, part of our proofs is based on new results. The relative Hodge-Tate
spectral sequence is new in this approach.
