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affine morphisms

DEFINITION 8.1   Let $ X$ be a scheme. Let $ \mathcal A$ be a quasi coherent sheaf with an $ \mathcal{O}_X$ -bilinear multiplication so that it is a sheaf of (unital associative) algebras. Then we may construct a scheme $ \operatorname{Spec}(\mathcal A)$ over $ X$ . The morphism $ \operatorname{Spec}(\mathcal A)\to X$ is called an explicit affine morphism. A morphism which is isomorphic to an explicit affine morphism so defined is called an affine morphism.



2007-12-11