Timeline for Is Mazur's analogy between arithmetic and topology formal, in any sense?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2022 at 16:16 | vote | accept | Matthew Niemiro | ||
| Jan 3, 2022 at 4:41 | comment | added | Will Sawin | @RyanBudney Certainly I do not have a proof that no category defined via three-manifolds could ever be equivalent to a category defined via number fields! | |
| Jan 3, 2022 at 4:35 | comment | added | Will Sawin | @Kapil Sure, I'm pretty sure not every space with cohomological dimension 3 has a duality for the category of sheaves with dualizing complex a locally constant sheaf of rank one shifted by 3. | |
| Jan 3, 2022 at 4:28 | comment | added | Kapil | In particular, is the statement anything more than the assertion that some cohomological dimension is 3? | |
| Jan 3, 2022 at 3:14 | comment | added | Ryan Budney | There is perhaps an equivalence of categories going on, but it won't be exactly the pair (3-manifolds, number fields). Likely you'll have to slightly change both categories to find a proper equivalence. At least, that's my suspicion. Or a more negative way to look at this is that categories may be fairly limited in what they can see, and that a subject area having a few key theorems forces a coarse structure on a category. | |
| Jan 3, 2022 at 1:38 | history | answered | Will Sawin | CC BY-SA 4.0 |