Timeline for Is good reduction decidable?
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5 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2020 at 23:23 | comment | added | Gro-Tsen | @Asvin Right, although the emphasis isn't so much on “countable” (although this is certainly a prerequisite) as on the fact that the relevant data (schemes, morphisms between them, etc.) can be indeed represented by computer. | |
| Aug 11, 2020 at 23:20 | comment | added | Gro-Tsen | @LSpice Well, yes and no. Once it is checked that these various algebraico-geometric objects can be represented by finitistic data that can be manipulated by a Turing machine, it's straightforward to just enumerate all possible such data. What isn't obvious is that they can indeed be represented (well, for $\mathscr{X}$ it is by the definition of “projective”). For this, see §16 of my joint paper with F. Orgogozo (not claiming originality here, it was probably considered folklore). | |
| Aug 11, 2020 at 23:18 | comment | added | Asvin | I think so. We have to iterate over possible dimensions and for each dimension, the base ring is countable so there are countably many projective schemes and given $X_\eta,X$, morphism between them are another countable family. | |
| Aug 11, 2020 at 23:08 | comment | added | LSpice | Is it obvious that all those collections are enumerable? | |
| Aug 11, 2020 at 23:06 | history | answered | Gro-Tsen | CC BY-SA 4.0 |