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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

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 \(L(s, \chi)\)

Citations:

Zbl 0538.00016