Timeline for Absolute approximation of formal schemes
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 19, 2018 at 2:49 | comment | added | nfdc23 | @AntonFetisov: If someone else wants to do so then that is fine by me. The question as posed seemed like asking for way too much (mixing apples and oranges in terms of completeness and direct limits). | |
| May 16, 2018 at 10:43 | comment | added | Anton Fetisov | @nfdc23 , would you mind turning your comment into an answer? | |
| May 15, 2018 at 12:37 | comment | added | nfdc23 | No, if "$p$-adic formal scheme" entails $p$-adic completions everywhere (to make the inverse limit categorical). Endomorphisms of the structure sheaf as a module over itself is "global sections", so $\mathfrak{X}_j = {\rm{Spf}}(O_{K_j})$ for the directed system of finite extensions $K_j$ of $\mathbf{Q}_p$ inside an algebraic closure (so $\mathfrak{X}= {\rm{Spf}}(O_{\mathbf{C}_p})$) is a counterexample for morphisms. Via the formal affine lines $\mathfrak{X}_j={\rm{Spf}}(O_{K_j}\{t\})$ it fails on objects: $O_{\mathbf{C}_p}\{t\}/(t-a)$ for $a\in \mathfrak{m}$ not algebraic over $\mathbf{Q}_p$. | |
| May 15, 2018 at 11:39 | history | edited | user95222 | CC BY-SA 4.0 |
added 2 characters in body
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| May 15, 2018 at 8:01 | history | asked | user95222 | CC BY-SA 4.0 |