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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)

MSC:
 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 Étale 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)