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8
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Accepted
A noneffective descent datum: isomorphism not satisfying the cocycle condition
This already fails for line bundles on smooth projective curves: let $X$ be 'the' pointless conic over $\mathbb{R}$, given by the closed subscheme of $\mathbb{P}^2_{\mathbb{R}}$ cut out by $X^2+Y^2+Z^ …