2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112915This article is the last one about the isomorphism between Lubin-Tate and Drinfeld towers. We prove the existence of an isomorphism between the compactly supported etale cohomology of the Lubin-Tate and Drinfeld towers, and more generally their equivariant cohomology complex. We also prove the existence of a geometric local Jacquet-Langlands correspondence between some equivariant rigid etale sheaves on Gross-Hopkins period space $\mathbb{P}^{n-1}$ and Drinfeld one $Ω$.72 pagesNumber TheoryAlgebraic Geometry14Gxxtext