If I have a morphism of schemes $f: X \rightarrow S$ and a point $s$ in $S$, then I can consider the fibre $X_s$ over that point.
If $x$ is a point in $X$ which is also (topologically) in $X_s$, is then the residue field of $x$ as point in $X$ and as point in $X_s$ the same?
Of course, I tried to solve it locally, but was confused by the many localizations and possible isos. Perhaps you can give a hint if the statement is true and a short note how to show it.
Thanks!