Unstable operations in etale and motivic cohomology

Chuck Weibel, Rutgers University
Fine Hall 314

Epstein constructed cohomology operations $P^i$ in etale cohomology, and Voevodsky constructed cohomology operations $P^i$ in motivic cohomology. These differ from the topological operations because of twisting. We modify Henri Cartan's classification of unstable operations to classify all etale operations (they are the expected operations), and classify all weight one motivic operations. Here new operations arise, and we paint a conjectural picture in all weights. This is joint work with Bert Guillou.