Lectures on motivic cohomology 2000/2001 (written by Pierre Deligne)

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These lecture notes cover four topics. There is a proof of the fact that the functors represented by the motivic Eilenberg-Maclane spaces on the motivic homotopy category coincide with the motivic cohomology defined in terms of the motivic complexes. There is a description of the equivariant motivic homotopy category for a finite flat group scheme (over a noetherian base) together with a new characterization of A¹-equivalences. There is a part where we introduce a class of sheaves called solid sheaves. Finally there is a part where we study functors of the form X -> X/G and X -> Xʷ and show that they preserve equivalences between term-wise ind-solid simplicial sheaves.