Fiber of the map on spectra
= Fiber of the map on spectra
The fiber over $\mathfrak p\in\operatorname{Spec}A$ of $\operatorname{Spec}B\to\operatorname{Spec}A$ is the set of primes $\mathfrak q\subset B$ satisfying $\mathfrak q\cap A=\mathfrak p$. It is naturally the spectrum of the fiber ring $B\otimes_A\kappa(\mathfrak p)$.