Geodesic
Cancellation theorem
Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 671-685.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $$\underline{Hom}({\bold Z}_{tr}(X),{\bold Z}_{tr}(Y))\rightarrow \underline{Hom}({\bold Z}_{tr}(X)\otimes_{tr}{\bold G}_m,{\bold Z}_{tr}(Y)\otimes_{tr}{\bold G}_m)$$ is a (weak) ${\bold A}^1$-homotopy equivalence. As a corollary we deduce that the Tate motive is quasi-invertible in the triangulated categories of motives over perfect fields.
Classification : 14F42, 19E15 
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     author = {Voevodsky, Vladimir},
     title = {Cancellation theorem},
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Voevodsky, Vladimir. Cancellation theorem. Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 671-685. http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a1/