Timeline for Is there a reason for defining the differential forms before the vector fields ?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jun 3, 2010 at 20:40 | comment | added | Mike Skirvin | If $X/S$ is not smooth, it is common to consider the cotangent complex rather than $\Omega^1.$ This is a derived version of Kahler differentials that agrees with $\Omega^1$ if $X/S$ is smooth. You can then define the tangent complex to be the dual of the cotangent complex. On a ring theoretic level, this is related to what's known as Andre-Quillen (co)homology. | |
| Jun 3, 2010 at 20:23 | comment | added | Donu Arapura | I think it's useful, but one has to be more careful with it. | |
| Jun 3, 2010 at 20:07 | comment | added | user2330 | Yes, but, in the case $X/S$ not smooth, is $\Omega^1_{X/S}$ useful ? | |
| Jun 3, 2010 at 19:36 | comment | added | Mariano Suárez-Álvarez | I wonder if there are useful conditions for $\Omega^1$ to be reflexive... | |
| Jun 3, 2010 at 19:27 | history | answered | Donu Arapura | CC BY-SA 2.5 |