Lectures on algebraic cycles. (Q1598344)

This article is intended to ``give a survey of the subject on algebraic cycles to non-specialists, and from the point of view of a transcendental algebraic geometer.'' As a whole, it gives a readable introduction to the author's book [A survey of the Hodge conjecture, Second Edition (CRM Monograph Series 10, Providence, RI: AMS) (1999; Zbl 0922.14004)]. No matter when he tries to explain a general notion or theorem, he provides us with a motivating example or a brief but smart sketch of proof. The main topics dealt with are the following ones: Noether-Lefschetz theorem, Mumford's theorem on zero-cycles on surfaces and its several generalizations, extensions of mixed Hodge structures and a candidate Bloch-Beilinson filtration (together with recent contributions of the author himself), and a procedure for constructing indecomposables in \(K_m(X)\), \(m>1\) [J. Reine Angew. Math. 485, 162--172 (1997; Zbl 0868.14003)].