Chow-Witt groups and Grothendieck-Witt groups of regular schemes, by Jean Fasel and Vasudevan Srinivas

We show that the Chow-Witt groups can be defined using only the notion of Grothendieck-Witt groups of triangulated categories. As an application, we show that there is always a homomorphism from the top Chow-Witt group of a regular scheme to some Grothendieck-Witt group of this scheme. In dimension 3, we use this fact to prove that the vanishing of its Euler class is sufficient for a projective module of rank 3 with trivial determinant to have a free factor of rank one.

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