Erratum to the article: Global applications to relative $(\phi,\Gamma)$(φ,Γ)-modules

The present erratum is meant to correct two errors in the article \cite{andreatta_iovita1}. The first is an error in the definition of Faltings''s topology (\cite{andreatta_iovita1}, \S 4.2) and was pointed out to us by Ahmed Abbes and the second is the statement and proof of Proposition 4.4.2, 6) and 7).