The Topology of Algebraic Varieties
The Topology of Algebraic Varieties, 2014-15
Claire Voisin, Institut de Mathématiques de Jussieu, was the School's Distinguished Visiting Professor during the 2014-15 academic year. Professor Voisin led a special program on "The Topology of Algebraic Varieties". The topology of algebraic varieties is traditionally understood in two different senses: either one considers real or complex algebraic varieties, and then one studies (mostly via Hodge theory) the topology of (the set of real or complex points of) this algebraic variety, endowed with the Euclidean topology, or one studies this algebraic variety endowed with the Zariski or étale topology with the help of various cohomology theories (étale, de Rham...) The second viewpoint is closer in spirit to the theory of motives, as it includes the various comparison isomorphisms, and because it does not use non-algebraic data. The complex point of view is, in fact, also very well-adapted to the study of algebraic cycles, in view of the Bloch-Beilinson conjectures. This program intends to bring a mix of people interested in various aspects of the subject: Motives, K-theory, Chow groups, periods, fundamental groups.