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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?

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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 $f^{-1}(y)$.

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  • $\begingroup$ you could also mention reference so that it is useful for others :) Thanks $\endgroup$ Commented Jan 1, 2020 at 13:12

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