Homotopy invariance of the sheaf WNis and of its cohomology
نویسنده
چکیده
A conjecture of F.Morel states that the motivic group π0,0(k) of a perfect field k coincides with the Grothendieck-Witt group GW (k) of quadratic forms over k provided that char(k) 6= 2. Morel’s proof of the conjecture requires the the following result: the Nisnevich sheaf WNis associated with the presheaf X 7→ W (X) is homotopy invariant and all its Nisnevich cohomology are homotopy invariant too. A rather short and self-contained proof of the result is given here. Another proof is due to J.Hornbostel [H].
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تاریخ انتشار 2004