Title: The rise of motivic mathematics
Speaker: Charles Weibel
Speaker Info: Rutgers
In the 1960's, Grothendieck envisioned motives as something like a universal cohomology theory for algebraic varieties, using Chow groups.Date: Wednesday, October 23, 2019
In the 1990's, Voevodsky (then at Northwestern!) constructed what we now view as motivic cohomology, having many of the properties proposed by Grothendieck. Nowadays, the focus is on motivic homotopy theory, in which motivic cohomology plays the role of just one of many cohomology theories. Other generalized cohomology theories are inspired by topology, such as cobordism and K-theory. All this is needed to show that the étale cohomology of a field has a presentation by generators and relations.