Summary
A conjecture of F. Morel states that the motivic group π0, 0(k) of a field k coincides with the Grothendieck-Witt group GW(k) of quadratic forms over k provided that char(k)≠2. Morel’s proof of the conjecture is based among others on the the following result: the Nisnevich sheaf W Nis associated with the presheaf X↦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.
2010 Mathematics subject classification. 18F20, 14F42.
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Panin, I. (2010). Homotopy Invariance of the Sheaf W Nis and of Its Cohomology. In: Colliot-Thélène, JL., Garibaldi, S., Sujatha, R., Suresh, V. (eds) Quadratic Forms, Linear Algebraic Groups, and Cohomology. Developments in Mathematics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6211-9_21
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