L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld : demonstration du resultat principal

Abstract

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.