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Cancellation theorem. (English) Zbl 1202.14022
Summary: We give a direct proof of the fact that for any schemes of finite type \(X, Y\) over a Noetherian scheme \(S\) the natural map of presheaves with transfers \[ \underline{Hom}({\mathbf Z}_{tr}(X),{\mathbf Z}_{tr}(Y))\rightarrow \underline{Hom}({\mathbf Z}_{tr}(X)\otimes_{tr}{\mathbf G}_m,{\mathbf Z}_{tr}(Y)\otimes_{tr}{\mathbf G}_m) \] is a (weak) \({\mathbf A}^1\)-homotopy equivalence. As a corollary we deduce that the Tate motive is quasi-invertible in the triangulated categories of motives over perfect fields.

MSC:
14F42 Motivic cohomology; motivic homotopy theory
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
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