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On Open Embeddings of Affine Spaces in Affine Varieties and the Jacobian Conjecture
Let $k$ be a field of \uline{characteristic $0$}. Our final goal is the following faded problem~: {\sf The Jacobian Conjecture $(JC_2)$~:} {\it If $f_1, f_2$ are elements in a polynomial ring $k[X_1, X_2]$ over $k$ such that $ \det(\partial f_i/ \partial X_j) $ is a nonzero constant, then $k[f_1
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