  This is the fourth article about the isomorphism between Lubin-Tate and
Drinfeld towers. We prove the final result concerning the isomorphism that is
to say the existence of an equivariant isomorphism between some blow-up of the
formal scheme associated to Lubin-Tate space with infinite level constructed
cellularly before and a blow-up of another formal scheme associated to Drinfeld
tower. We follow the strategy of Gerd Faltings.
