Is there a scheme $X$ , $f \in \Gamma(X;\mathcal{O}_X)$ s.t. $\Gamma(X;\mathcal{O}_X)_f \to \Gamma(X_f ;\mathcal{O}_{X_f} )$ is not an equality?

Asked Apr 04 '20 at 06:06

Active Apr 04 '20 at 19:45

Viewed 91 times

I'm trying to understand if there exists a scheme $X$ and an $f \in \Gamma(X;\mathcal{O}_X)$ such that the natural map $\Gamma(X;\mathcal{O}_X)_f \to \Gamma(X_f ;\mathcal{O}_{X_f} )$ is not an equality ?

I think I need to look for something not affine, but I cannot think of the example, I will appreciate any help!

asked Apr 04 '20 at 06:06

Rainbow57

4

You're going to need to do a lot worse than just non-affine, see https://math.stackexchange.com/questions/2360435/qcqs-lemma-in-ravi-vakils-notes – KReiser Apr 04 '20 at 06:20

Is there a scheme $X$ , $f \in \Gamma(X;\mathcal{O}_X)$ s.t. $\Gamma(X;\mathcal{O}_X)_f \to \Gamma(X_f ;\mathcal{O}_{X_f} )$ is not an equality?

0 Answers0