Soulé, Christophe Cohomologie des groupes discrets et formes automorphes. (French) Zbl 0559.14013 Variétés de Shimura et fonctions L, Publ. Math. Univ. Paris VII, No. 6, 131-143 (1979). [For the entire collection see Zbl 0517.00003.] In the main part of the seminar of which this text is the last lecture the zeta function of a certain Shimura variety was expressed as the product of L-functions of automorphic representations [cf. J. P. Labesse, ibid., pp. 83-130 (1979; see the preceding review)]. In this lecture the connection of such formulas with the cohomology of arithmetic groups is (very roughly) sketched. Reviewer: J.G.M.Mars Cited in 1 Document MSC: 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols 11F70 Representation-theoretic methods; automorphic representations over local and global fields Keywords:zeta function; Shimura variety; product of L-functions; cohomology of arithmetic groups Citations:Zbl 0559.14012; Zbl 0517.00003 PDFBibTeX XML