Timeline for What is the precise relationship between o-minimal theory and Grothendieck's "Esquisse d'un programme"?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2016 at 13:37 | comment | added | ACL | @EmilJeřábek Thanks for the correction. I edited accordingly. | |
| Apr 21, 2016 at 10:26 | vote | accept | Mikhail Katz | ||
| Apr 20, 2016 at 20:07 | history | edited | ACL | CC BY-SA 3.0 |
edit: corrections of 2 mistakes indicated in comments
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| Apr 20, 2016 at 15:15 | comment | added | Mikhail Katz | @ACL, I take it you mean to take a complex analytic subset of $\mathbb{C}^n$. | |
| Apr 20, 2016 at 15:12 | comment | added | Emil Jeřábek | Definable functions needn’t be piecewise $C^\infty$. They are piecewise $C^k$ for every finite $k$, but you may need finer and finer pieces as $k$ gets larger. See the comments at mathoverflow.net/questions/234337 . | |
| Apr 20, 2016 at 15:01 | comment | added | ACL | It is not clear to me that this requirement in Grothendieck's esquisse (“passing from $X$ to $\mathop{\rm Aut}(X)$ leaves the world of finite dimensional spaces”, he says) is satisfied by o-minimal geometry. At least not obviously. | |
| Apr 20, 2016 at 14:59 | comment | added | Mikhail Katz | I take it the collection of all definable functions between fixed source and target is also definable? This would answer Grothendieck's dream and should probably be mentioned in the answer. | |
| Apr 20, 2016 at 14:58 | history | edited | ACL | CC BY-SA 3.0 |
add: complex algebraic in the statement of Peterzil-Starchenko
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| Apr 20, 2016 at 14:57 | comment | added | ACL | non, complex algebraic! I'll edit! | |
| Apr 20, 2016 at 14:48 | comment | added | Mikhail Katz | The conclusion of Petezil-Starchenko is real-algebraic? | |
| Apr 20, 2016 at 14:46 | comment | added | Mikhail Katz | The commands \\[ and \\] don't work at MO. | |
| Apr 20, 2016 at 14:45 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
edited body
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| Apr 20, 2016 at 14:42 | history | answered | ACL | CC BY-SA 3.0 |