Cancellation theorem, by Vladimir Voevodsky

We prove that for any two objects K and L of the category DM over a perfect field the map from Hom(K,L) to Hom(K(1),L(1)) is bijective. The proof is elementary in the sense that it uses only the basic properties of homotopy invariant presheaves with transfers and direct geometric arguments. The main part of the proof is given in the context of schemes of finite type over a noetherian base scheme.

Vladimir Voevodsky <>