Introduction et notes de cours de l'école d'été consacrée aux recherches récentes sur les catégories triangulées de motifs, sur la théorie homotopique des motifs bords et leurs applications et sur une version triangulée des conjectures de Tate et Beilinson sur les cycles algébriques sur les corps finis. ©Electre 2026

Quatrième de couverture

This volume contains the second part of the lectures notes of the Asian-French summer school on algebraic geometry and number theory, which was held at the Institut des Hautes Études Scientifiques (Bures-sur-Yvette) and the université Paris-Sud XI (Orsay) in July 2006. This summer school was devoted to the theory of motives and its recent developments, and to related topics, notably Shimura varieties and automorphic representations.

The contributions in this second part are expanded versions of the series of lectures by M. Levine on triangulated categories of motives and motivic homotopy of schemes (Six lectures on motives), and of the additional lectures by J. Wildeshaus on boundary motives and their applications (Boundary motives, relative motives and extensions of motives) and by B. Kahn on a triangulated version of the conjectures of Tate and Beilinson on algebraic cycles over a finite field (The full faithfullness conjectures in characteristic p).