Timeline for Regular holonomic D-modules as generalisation of regular singular points
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2017 at 23:12 | answer | added | Avi Steiner | timeline score: 3 | |
| Jun 16, 2017 at 9:57 | comment | added | C. Dubussy | @Avi Steiner : Thanks for your comment. I was aware of these equivalences but the definition with filtrations was the first to appear in Kashiwara's papers about the Riemann-Hilbert problem. And he said that this definition "clearly allows to recover the usual definition for differential equations". So perhaps it is the "best" definition to make the link with the old one. | |
| Jun 15, 2017 at 18:49 | comment | added | Avi Steiner | You might want to look into the other equivalent conditions. E.g.: 1) Every pullback to a smooth curve has all r.h. cohomology; 2) the analytic and formal power series solution complexes agree. | |
| Jun 15, 2017 at 13:59 | history | edited | C. Dubussy | CC BY-SA 3.0 |
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| Jun 15, 2017 at 13:57 | comment | added | C. Dubussy | You're right, I have been too quick, my filtration is not a good candidate. I will edit the post with your suggestion. The main problem for me is to prove the equality $f\cdot \text{gr}(M)=0$. | |
| Jun 15, 2017 at 13:54 | comment | added | Simon Wadsley | Also note that your statement says that there exists a good filtration with some property not that every good filtration has that property. | |
| Jun 15, 2017 at 13:54 | comment | added | Simon Wadsley | I think you are mistaken that your filtration is good. You want something like $M_n=D_n.(1+D_\mathbb{C}P)$ where $D_n$ denotes the differential operators of order at most $n$. You will only get $M_n=M$ for some $n$ if $M$ is an integrable connection ie a f.g. $O_X$-module. | |
| Jun 15, 2017 at 13:19 | history | asked | C. Dubussy | CC BY-SA 3.0 |