Timeline for Interpretation of model theory in algebraic geometry
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 26 at 22:52 | comment | added | Alex Kruckman | @DonuArapura That's right, no negations. | |
| Feb 26 at 22:24 | comment | added | Donu Arapura | @AlexKruckman OK, thanks for the comment. I hadn't realized that there was a strong statement. I assume "positive" means no negations. | |
| Feb 26 at 16:16 | comment | added | Alex Kruckman | @DonuArapura That's true, but the model-theoretic proof uses a refinement of the idea of quantifier elimination, namely that if a formula is preserved by all homomorphisms from subrings to algebraically closed fields (rather than all embeddings from subrings to algebraically closed) then it is equivalent to a positive quantifier-free formula, and as a consequence, it defines a Zariski-closed set, rather than just a constructible set. | |
| Feb 21 at 14:54 | history | edited | Alex Kruckman | CC BY-SA 4.0 |
fixed a crucial typo in the last line
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| Feb 21 at 14:49 | history | edited | Alex Kruckman | CC BY-SA 4.0 |
cleaned up post, fixed typos, added a link to the paper, etc.
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| Feb 21 at 14:48 | comment | added | Donu Arapura | I admit that I haven't had the time or energy to read your question carefully. But probably yes: elimination of quantifiers for algebraically closed fields on the model theory side is equivalent in algebraic geometry to the fact the class of constructible sets is stable under projections. | |
| Feb 21 at 12:56 | history | asked | George | CC BY-SA 4.0 |