Soulé, Christophe On K-theory and values of zeta functions. (English) Zbl 0558.12004 Current trends in algebraic topology, Semin. London/Ont. 1981, CMS Conf. Proc. 2, 1, 49-58 (1982). [For the entire collection see Zbl 0538.00016.] Some of the most interesting recent research in algebraic K-theory has been motivated by the conjectured connection between the orders of K- groups of rings of algebraic integers and the values of the zeta functions of their number fields. This article surveys these conjectures in a concise yet thorough way, and discusses their extension to curves and other varieties over a finite field. Reviewer: M.R.Stein Cited in 1 Document MSC: 11R70 \(K\)-theory of global fields 11R42 Zeta functions and \(L\)-functions of number fields 14G15 Finite ground fields in algebraic geometry 18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) 14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry 11M06 \(\zeta (s)\) and \(L(s, \chi)\) Keywords:Lichtenbaum conjectures; varieties over finite field; algebraic K-theory; rings of algebraic integers; zeta functions Citations:Zbl 0538.00016 PDFBibTeX XML