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About: Jouanolou's trick     Goto   Sponge   NotDistinct   Permalink

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In algebraic geometry, Jouanolou's trick is a theorem that asserts, for an algebraic variety X, the existence of a surjection with affine fibers from an affine variety W to X. The variety W is therefore homotopy-equivalent to X, but it has the technically advantageous property of being affine. Jouanolou's original statement of the theorem required that X be quasi-projective over an affine scheme, but this has since been considerably weakened.