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 $\kappa (s)$.