De Rham cohomology of Lubin-Tate spaces and Drinfeld spaces

Abstract

Let $d\ge 1$ be an integer. We use the methods introduced by Lue Pan to prove that the compactly supported cohomology of Lubin-Tate towers and Drinfeld towers are isomorphic, as $\text{GL}_{d+1}(L)\times D_{L,\frac{1}{d+1}}^\times$-modules.