Topics in algebraic geometry
For Ph.D. students. I require a good knowledge of algebraic intersection theory, as developed in Fulton's Intersection theory.
Review of intersection theory. The category of correspondences. Pure motives. Finite dimensionality of pure motives. The standard conjectures. Chow-Künneth decomposition. The Bloch-Beilinson filtration, and its consequences.
Jacob P. Murre, Jan Nagel, Chris A.M. Peters, Lectures on the theory of pure motive, University Lecture Series, 61, American Mathematical Society (2013).
Yves André , Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panoramas et Synthèses, 17, Paris: Société Mathématique de France (2004).