About the Bloch and Kato conjectures: Galois cohomology and values of \(L\)-functions. (Autour des conjectures de Bloch et Kato: Cohomologie galoisienne et valeurs de fonctions \(L\).) (French) Zbl 0821.14013

Jannsen, Uwe (ed.) et al., Motives. Proceedings of the summer research conference on motives, held at the University of Washington, Seattle, WA, USA, July 20-August 2, 1991. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 55, Pt. 1, 599-706 (1994).
This article is of expository nature and explains the authors’ generalisation of the Bloch-Kato theory. The first section explains various local \(l\)-adic cohomologies, the second the globalisation, and the third the conjectures on \(L\)-functions and Tamagawa numbers.
For the entire collection see [Zbl 0788.00053].
Reviewer: G.Faltings (Bonn)


14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
11R34 Galois cohomology
14F30 \(p\)-adic cohomology, crystalline cohomology
19F27 √Čtale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)
11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11S25 Galois cohomology
14A20 Generalizations (algebraic spaces, stacks)