Integral $p$-adic \'etale cohomology of Drinfeld symmetric spaces

We compute the integral p-adic etale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational p-adic etale cohomology from our recent work on Stein spaces. The main tools are: the computation of the integral de Rham cohomology from that work and, as a new tool, the integral p-adic comparison theorems of Bhatt–Morrow–Scholze and Cesnavicius–Koshikawa which replace the quasi-integral comparison theorem of Tsuji. Along the way, we compute the A inf -cohomology of Drinfeld symmetric spaces.