## morphism in algebraic geometry [closed]

In algebraic geometry, there is a question confuses me: the morphism between two scheme is defined algebraically in terms of morphism of structure sheaf, but how can we show any morphism of structural sheaf corresponding to a (geometrically) morphism between schemes (geometrically means we glue local model and the morphism is defined in terms of polynomial functions)? I didn't see such a proof. Can we do this similarly in differential category?

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 Your question is not precise and besides I doubt that it is research level. – Martin Brandenburg Dec 11 2010 at 10:14 Please reexamine the definition of morphism in your textbook, or on Wikipedia. If you want to turn your question to a well-defined one, please click the "edit" link, and type in the appropriate changes. – S. Carnahan♦ Dec 11 2010 at 12:06