Timeline for Dolbeault cohomology of $\text{sl}(2,\mathbb{C})$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 30, 2017 at 0:49 | comment | added | C. Dubussy | @Mohan Ramachandran : Thank you very much. | |
| Jun 29, 2017 at 20:26 | comment | added | Mohan Ramachandran | @C.Dubussy . Serre's paper is titled Un Theoreme de Dualite Commentarii Mathematici Helvetici vol 29 (1955) 9-26 . | |
| Jun 29, 2017 at 2:44 | comment | added | C. Dubussy | @Mohan Ramachandran : Could you tell me the exact title of the paper ? Also note that I'm not interested in $H^*_c$ but $H^*_F$. | |
| Jun 28, 2017 at 19:08 | comment | added | Mohan Ramachandran | Since G is stein you can find compactly supported cohomology .See Theorem 3 of Serre's paper on Serre duality. | |
| Jun 28, 2017 at 18:25 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Jun 28, 2017 at 14:34 | comment | added | C. Dubussy | Thank you for your comment. I was guessing that the first question was particularly trivial. Do you have any idea for the second one ? | |
| Jun 28, 2017 at 14:22 | comment | added | Jason Starr | This is the underlying complex analytic space of a complex affine variety, hence it is Stein. Therefore all of the higher cohomology groups of all coherent analytic sheaves are zero. Since $\Omega$ has a canonical left-invariant isomorphism with the sheaf of holomorphic functions into the one-dimensional complex vector space $\bigwedge^3_{\mathbb{C}} \mathfrak{sl}_2(\mathbb{C})$, the global sections of $\Omega$ are just the holomorphic functions on this complex Lie group. | |
| Jun 28, 2017 at 14:18 | history | asked | C. Dubussy | CC BY-SA 3.0 |