Timeline for Formally smooth morphisms, the cotangent complex, André-Quillen cohomology, and representability of nilpotent extensions as trivial extensions over a cofibrant replacement
Current License: CC BY-SA 2.5
20 events
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| Nov 13, 2010 at 23:19 | vote | accept | Harry Gindi | ||
| Nov 13, 2010 at 23:19 | history | bounty ended | Harry Gindi | ||
| Nov 13, 2010 at 23:03 | answer | added | Charles Rezk | timeline score: 7 | |
| Nov 13, 2010 at 22:14 | comment | added | Harry Gindi | I may have neglected to point out that an extension of the form $S\oplus M$ is called a trivial extension of $S$, and that these can be identified exactly with the nilpotent extensions of $S$ admitting a section that is a morphism of $A$-algebras. See $EGA0_{IV}.18$ or M. André's book Homologie des Algèbres Commutatives Ch. 16. | |
| Nov 13, 2010 at 21:33 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 13, 2010 at 21:28 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 13, 2010 at 21:23 | history | bounty started | Harry Gindi | ||
| Nov 11, 2010 at 21:16 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 11, 2010 at 21:11 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 10, 2010 at 15:06 | comment | added | S. Carnahan♦ | You can put his name back in with a suitable invocation of "André-Quillen". | |
| Nov 10, 2010 at 12:12 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 10, 2010 at 11:55 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 10, 2010 at 11:45 | comment | added | Graham Leuschke | The construction on $R\oplus M$ is not due to Quillen. It goes back at least to Dorroh in the 30s, was named the 'trivial extension' by Hochschild in the 50s, and was popularized in commutative algebra by Nagata's book. | |
| Nov 10, 2010 at 10:23 | history | edited | Harry Gindi |
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| Nov 10, 2010 at 9:35 | comment | added | Harry Gindi | (I'm 99% sure that the module in question is $T/J\otimes_T \Omega_{T/R}$) | |
| Nov 10, 2010 at 9:20 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 10, 2010 at 9:07 | comment | added | Harry Gindi | (I think that the reason why we can characterize unramified morphisms in this way is as follows (I don't remember the argument, but I could work it out): I think we can always find a $T/J$-module $M$ such that $T$ is a subring of $T/J\oplus M$, so if the claim holds for square-zero extensions of $T/J$ representing modules, it implies the general case by the fact that inclusions are monic.) | |
| Nov 10, 2010 at 9:02 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 10, 2010 at 8:30 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Nov 10, 2010 at 8:25 | history | asked | Harry Gindi | CC BY-SA 2.5 |