= GAGA theorem
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= GAGA
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{synonym}
For a projective variety over the complex numbers, analytification gives an equivalence between algebraic and analytic <coherent sheaves>, preserves their cohomology, and is fully faithful on their morphisms. In particular, a holomorphic isomorphism between algebraic <line bundles> is algebraic. This allows a complex-torus proof of a line-bundle identity to establish the corresponding algebraic identity on a projective <elliptic curve>.
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