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I am reading INTERSECTION THEORY (Fulton), I am in page 15 and I do not understand the meaning of : SCHEME-THEORIC FIBER (I know what is a fiber, but what does scheme-theoric means?

Roxana
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  • I would suggest looking at https://math.stackexchange.com/questions/607934/underlying-set-of-the-scheme-theoretic-fiber and https://math.stackexchange.com/questions/322188/how-to-compute-the-topological-space-of-fibered-product-of-schemes – Praphulla Koushik Jan 01 '20 at 13:12

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In algebraic geometry, the scheme-theoretic fiber of a morphism of schemes $f: X \to Y$ at $y$ is the fiber product $\kappa(y) \times_Y X$ where $\kappa(y)$ is the residue field at $y$. This is a fiber product in the category of scheme and is a scheme whose underlying topological space is homeomorphic to $f^{-1}(y)$.