Cohomologie des espaces symétriques de Drinfeld et cocycles harmoniques

We show that the cohomology groups of the Drinfeld symmetric space $\text{Ω}{}^{\mathrm{(n+1)}}$ defined over a local field of any characteristic are GL_n+1-isomorphic to certain spaces of harmonic cochains on the Bruhat–Tits building. To cite this article: Y. Aït Amrane, C. R. Acad. Sci. Paris, Ser. I 338 (2004).