Definition 26.18.4. Let f : X \to S be a morphism of schemes. Let s \in S be a point. The scheme theoretic fibre X_ s of f over s, or simply the fibre of f over s, is the scheme fitting in the following fibre product diagram
\xymatrix{ X_ s = \mathop{\mathrm{Spec}}(\kappa (s)) \times _ S X \ar[r] \ar[d] & X \ar[d] \\ \mathop{\mathrm{Spec}}(\kappa (s)) \ar[r] & S }
We think of the fibre X_ s always as a scheme over \kappa (s).
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