Timeline for cotangent complex of a trivial extension
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2013 at 5:03 | answer | added | rrrrrttttttt | timeline score: 1 | |
| Mar 19, 2011 at 18:59 | comment | added | Bhargav | I think one possible general answer is that L_{B/A} (with B = A + M) has good connectivity properties if M does so. These issues were discussed in what used to be Lurie's DAG IV, and I suspect can also be found in his "Higher Algebra" book (but I did not look). | |
| Mar 19, 2011 at 12:43 | comment | added | Martin Lagenbach | Thanks a lot Bhargav. I am such an idiot! I guess I was computing the case $A=k$ and any $M$, but I was computing the $H^0$ i.e. the Kahler differentials. Sorry about being so sloppy. By the way, do you have a guess for a general answer? | |
| Mar 18, 2011 at 21:54 | comment | added | Bhargav | Unless I'm mistaken, this already fails in the discrete case. Take A = k, and M = k. Then B := A + M is k[e]/(e^2), and the cotangent complex of B/A (computed using the transitivity triangle for k -> k[e] ->> B) is quasi-isomorphic to the 2-term complex given by multiplication by d(e^2) = 2e on B. In particular, it has two non-zero homology groups as a complex of k-vector spaces. | |
| Mar 18, 2011 at 19:08 | history | asked | Martin Lagenbach | CC BY-SA 2.5 |