= Generic fiber
{title2=$X_\eta=X\times_S\operatorname{Spec}\kappa(\eta)$}
= Generic fibre
{synonym}
For a <morphism of schemes> $X\to S$ with $S$ an <integral scheme> and <generic point> $\eta$, the generic fiber is its <scheme-theoretic fiber> over $\eta$. On <affine schemes> $S=\operatorname{Spec}A$ and $X=\operatorname{Spec}B$, it is $\operatorname{Spec}(B\otimes_A\operatorname{Frac}A)$. It can be empty, and it need not be a <reduced scheme> or an <irreducible scheme> without further assumptions.
Back to article page
