Timeline for The "unification" of geometry via topos theory?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| S Apr 5, 2021 at 3:02 | history | bounty ended | CommunityBot | ||
| S Apr 5, 2021 at 3:02 | history | notice removed | CommunityBot | ||
| S Mar 28, 2021 at 1:22 | history | bounty started | xuq01 | ||
| S Mar 28, 2021 at 1:22 | history | notice added | xuq01 | Draw attention | |
| Mar 26, 2021 at 0:51 | comment | added | xuq01 | @IngoBlechschmidt Thanks Ingo. Your thesis is truly a source of inspiration. I was wondering if we can go as far as things like e.g. differential forms and deformation theory, but I guess that's way, way ahead. | |
| Mar 25, 2021 at 21:20 | comment | added | Ingo Blechschmidt | Yes, we can! For instance, the same internal proof shows that, in AG, the Grassmannian is a smooth scheme over the base, and in DG, the Grassmannian is a smooth manifold (see Section 20.3 of these notes of mine). However, as you say, this approach is limited, the internal world of the toposes used in AG does differ quite a bit from their DG counterpart. For instance, in the toposes for AG, any map $R \to R$ is a polynomial. A generalization of this observation is the basis for synthetic AG, yet totally false for SDG. | |
| Mar 25, 2021 at 13:50 | history | edited | LSpice | CC BY-SA 4.0 |
[this one] -> question text
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| Mar 25, 2021 at 12:20 | history | asked | xuq01 | CC BY-SA 4.0 |