Timeline for Homotopical interpretation of flatness?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 26, 2016 at 19:29 | vote | accept | Arrow | ||
| Dec 26, 2016 at 19:02 | answer | added | skd | timeline score: 5 | |
| Jun 22, 2016 at 14:11 | comment | added | AAK | Flatness is equivalent to vanishing of all higher Tor groups, which are the same as the homology groups of derived tensor products, and derived tensor products are homotopy pushouts of commutative dg-algebras. A homotopical characterization of étaleness or smoothness can be given using the cotangent complex. See any of the usual references on derived algebraic geometry, e.g. Lurie's thesis or HAG II by Toen-Vezzosi. This all goes back to Quillen, whose original notes on homotopical algebra and the cotangent complex are also very good. | |
| Jun 22, 2016 at 10:05 | history | asked | Arrow | CC BY-SA 3.0 |