Timeline for What is the precise relationship between pyknoticity and cohesiveness?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 10, 2020 at 13:27 | comment | added | David Corfield | 'condensed sets are meant to be "the topos of spaces" '. What conclusion was reached as to pyknotic/condensed sets and being a Grothendieck/elementary topos? And then similarly for pyknotic/condensed anima/infinity-groupoids and Grothendieck/elementary infinity-toposes? | |
| Apr 9, 2020 at 15:45 | comment | added | Peter Scholze | Actually, when I gave my course on condensed mathematics I was quite amazed how abstractly developing the desired $6$-functor formalism for coherent duality was almost automatically leading one to rediscover (discrete) adic spaces, in particular the seemingly obscure conditions on $A^+\subset A$ -- an open and integrally closed subring of powerbounded elements. | |
| Apr 9, 2020 at 15:42 | comment | added | Peter Scholze | Thanks for your excitement :-)! Let me also point to work of Ben-Bassat and Kremnizer. These works are generally based on Banach or (dual) Frechet algebras, and I would expect that all of these theories can be embedded into our category of analytic spaces. However, these theories are generally less expressive than adic spaces (and as is well-known, I really like those) as they cannot talk about the second component of a Huber pair $(A,A^+)$, while our notion of analytic spaces is able to handle adic spaces in a very clean way. | |
| Apr 9, 2020 at 1:01 | comment | added | Emily | I just learned about your and Dustin Clausen's work on analytic geometry; it would be an understatement to say that it is amazing! Would it be ok to ask a question about it? From what I understand, this version of analytic geometry includes many other theories as special cases, such as smooth and complex manifolds as well as Berkovich spaces or schemes. Q: How is your and Clausen's theory related to other recent approaches to combining algebraic and p-adic geometries, such as e.g. Paugam or Poineau's work on global analytic geometry? | |
| Apr 9, 2020 at 0:59 | history | bounty ended | Emily | ||
| Apr 9, 2020 at 0:59 | vote | accept | Emily | ||
| Apr 7, 2020 at 13:10 | history | answered | Peter Scholze | CC BY-SA 4.0 |