MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X:=Spa A$ be an affinoid adic space, and $\underline X $ the ringed space of $X$. Let $Y:=Spec B$ be an affine scheme, $f: \underline X \longrightarrow Y$ a morphism of ringed spaces.

How to define a morphism of rings $g: B \longrightarrow A$ such that $f$ is induced by $g$?

share|cite|improve this question
What's wrong with the obvious morphism between rings of global sections? – Jérôme Poineau Apr 29 '13 at 8:35
@Jérôme Poineau: the global section of $SpaA$ is $\hat A$, so there is $B \longrightarrow \hat A$. – kiseki Apr 29 '13 at 13:26
Then I am not sure that it is possible to find such a morphism. How would you find $\hat{A} \to A$ that induces $\mathrm{Spa}A \simeq \mathrm{Spa}\hat{A} \to \mathrm{Spec}\hat{A}$? – Jérôme Poineau Apr 29 '13 at 15:39

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.