Lemma 26.20.4. Let $S$ be a scheme. Let $s' \leadsto s$ be a specialization of points of $S$. Then
there exists a valuation ring $A$ and a morphism $f : \mathop{\mathrm{Spec}}(A) \to S$ such that the generic point $\eta $ of $\mathop{\mathrm{Spec}}(A)$ maps to $s'$ and the special point maps to $s$, and
given a field extension $\kappa (s') \subset K$ we may arrange it so that the extension $\kappa (s') \subset \kappa (\eta )$ induced by $f$ is isomorphic to the given extension.
Comments (2)
Comment #4996 by Jérôme Poineau on
Comment #5236 by Johan on