0

I am trying to show that for an affine algebraic set $V\subset K^n$ with $K$ algebraically closed, $$\operatorname{Shv}(V;\mathcal{C})\simeq\operatorname{Shv}(\operatorname{Spec}(\mathcal{O}_V);\mathcal{C}),$$ where $\mathcal{C}$ is any category.

I know that we have to find a fully faithful functor $F:\operatorname{Shv}(V;\mathcal{C})\to\operatorname{Shv}(\operatorname{Spec}(\mathcal{O}_V);\mathcal{C})$, but I am unable to figure out this functor. Can somebody please help me? And, please elaborate your statements.

Anish Ray
  • 857
  • @KReiser Pardon me, but I have started studying Algebraic Geometry recently and I really don't understand most of the proof that you have mentioned. So, if you can kindly explain it to me in the context of my question it would be really helpful. Thank you – Anish Ray Nov 21 '21 at 20:21
  • Having re-read my answer there, I think it's pretty clear what's going on. If you don't understand portions of the proof, I might be willing to discuss a few questions about the specifics, but I'm not really up for re-explaining the whole thing to you: that's what the answer is for. – KReiser Nov 21 '21 at 21:53

0 Answers0