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

We think of the fibre $X_ s$ always as a scheme over $\kappa (s)$.

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