Timeline for Intrinsic topology on the Zariski spectrum
Current License: CC BY-SA 4.0
12 events
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| Mar 1, 2023 at 13:23 | history | edited | Peter Scholze | CC BY-SA 4.0 |
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| Mar 1, 2023 at 10:42 | comment | added | Zhen Lin | I think the constructively correct way of constructing the prime spectrum of a ring is by looking at prime filters rather than prime ideals. A prime filter is a multiplicatively closed subset containing $1$ and such that if $a + b$ is a member, then at least one of $a$ or $b$ are members. Of course, this is classically equivalent to being the complement of a prime ideal, so I suppose in a context with enough points it is equivalent to speak of ideals whose complements are multiplicatively closed and contain $1$. | |
| Mar 1, 2023 at 10:20 | comment | added | Ivan Di Liberti | As I discuss also in "The geometry of coherent topoi and ultrastructures", one should also acknowledge the work of Marmolejo on this topic, besides Makkai, Lurie and Barwick-Haine. | |
| Feb 28, 2023 at 20:14 | comment | added | Peter Scholze | Yes. The condensed structure it acquires gives the constructible topology of $\mathrm{Spec}(A)$. To see the actual Zariski topology, it is then sufficient to remember the specializations, recorded in the poset structure. | |
| Feb 28, 2023 at 20:11 | comment | added | Mike Shulman | Just so I understand completely: are you saying that the internal spectrum constructed in condensed sets does not get the condensed structure induced from the open-set Zariski topology in the naive way, but that it is instead the "correct" condensed structure in a different sense? | |
| Feb 27, 2023 at 22:12 | history | undeleted | Peter Scholze | ||
| Feb 27, 2023 at 22:11 | history | edited | Peter Scholze | CC BY-SA 4.0 |
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| Feb 27, 2023 at 22:00 | history | deleted | Peter Scholze | via Vote | |
| Feb 27, 2023 at 21:55 | history | undeleted | Peter Scholze | ||
| Feb 27, 2023 at 21:55 | history | edited | Peter Scholze | CC BY-SA 4.0 |
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| Feb 27, 2023 at 21:45 | history | deleted | Peter Scholze | via Vote | |
| Feb 27, 2023 at 21:41 | history | answered | Peter Scholze | CC BY-SA 4.0 |