Timeline for Why is the definition of the adic spectrum $\operatorname{Spa}\,(A,A^+)$ the "right" definition?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2023 at 23:27 | vote | accept | Krill | ||
| Mar 30, 2023 at 15:56 | answer | added | tkr | timeline score: 13 | |
| Mar 27, 2023 at 16:32 | comment | added | Krill | @TabesBridges I do indeed like this as a general explanation, but it would be nice to see an explicit example of when non-continuous valuations give us "the wrong thing" or something like that. | |
| Mar 27, 2023 at 16:31 | comment | added | Krill | @Satan'sMinion that is helpful for explaining the $A^+$. I'd have to see explicitly what's going on, but that's a good justification. Thanks for mentioning this resource, I hadn't been using them as much. | |
| Mar 25, 2023 at 13:38 | comment | added | Satan's Minion | Did you read section 3.3 in the Berkeley lectures? | |
| Mar 25, 2023 at 6:59 | comment | added | Z. M | One "reason" for continuous valuations is that, if I understand correctly, they are precisely points of the distributive lattice generated by basic open subsets (whose definition does not really depend on points). | |
| Mar 25, 2023 at 5:40 | comment | added | Tabes Bridges | Regarding your first question: I know nothing about these things, but given that the rings involved are topological, it would make sense to only consider valuations that in some way acknowledge the topology. | |
| Mar 25, 2023 at 2:41 | history | asked | Krill | CC BY-SA 4.0 |