Special values of \(L\)- functions of motives. (Valeurs spéciales des fonctions \(L\) des motifs.) (French) Zbl 0799.14006

Séminaire Bourbaki, Vol. 1991/92. Exposés 745-759 (avec table par noms d’auteurs de 1948/49 à 1991/92). Paris: Société Mathématique de France, Astérisque. 206, 205-249 (Exp. No. 751) (1992).
The author explains the various conjectures (Beilinson, Bloch-Kato, and others) relating special values of \(L\)-series and arithmetic cohomology groups. For the moment the theorems in the theory are rather rare, and deal mostly with compatibilities or special examples. However we have a good guess of what more advanced civilizations might be able to prove. In any case a good guide to the literature.
For the entire collection see [Zbl 0772.00016].
Reviewer: G.Faltings (Bonn)


14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14A20 Generalizations (algebraic spaces, stacks)
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