Über die Kohomologie einiger arithmetischer Varietäten. I
The goal of this paper is the computation of the (étale) cohomology of certain arithmetic varieties, which can be obtained as quotients of a product of several p-adic ''upper half planes'' by appropriate arithmetic groups, in particular unit groups of quaternion algebras. Though the situation differs from the corresponding classical one, because the p-adic ''upper half-plane'' has non trivial étale cohomology the final relation of the étale cohomology of the quotient \(\chi_{\Gamma}\) to the cohomology of the discrete group parallels exactly the corresponding classical results of \textit{Y. Matsushima} and \textit{G. Shimura} [Ann. Math., II. Ser. 78, 417-449 (1963; Zbl 0141.387)].
scientific article; zbMATH DE number 3904737