Timeline for Can the functor of the points of a scheme be characterized by its values on subcategories of the affine schemes?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 26, 2022 at 17:34 | comment | added | Will Sawin | @Z.M Yes, I think if you look in foundational works on deformation theory you will find such a theorem in there somewhere! | |
| Oct 26, 2022 at 17:33 | comment | added | Will Sawin | @MarsaultChabat I think not, unless you restrict the ideal with respect to which the ring underlying the affine scheme is complete. For residue field $k$ infinite, every smooth affine curve with infinitely many $k$-rational points gives the same functor. | |
| Oct 26, 2022 at 15:27 | comment | added | Z. M | But there might be criteria for (pro-)representability by formal schemes, I guess? This setups look very similar to deformation theory, where the "affines" are complete guys. | |
| Oct 26, 2022 at 15:24 | comment | added | Marsault Chabat | thank you for your answer. Sorry to keep asking, I trust you but I need to know at least the possible cases. If we consider an affine scheme whose underlying ring is a complete Noetherian ring, then can we recover the scheme only with its functor restricted on the complete local Noetherian rings? | |
| Oct 26, 2022 at 13:04 | history | answered | Will Sawin | CC BY-SA 4.0 |