Timeline for Sebastiani-Thom isomorphism for D-modules
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2020 at 19:56 | review | Suggested edits | |||
| Jan 9, 2020 at 20:21 | |||||
| Oct 1, 2013 at 20:15 | comment | added | Will Sawin | I believe this fails for the case $X = \mathbb C$, $f=g=id$, when $M$ and $N$ have non-regular singularities, e.g. already at the kernel of the differential operator $\left(\frac{d}{x} - \frac{1}{x^2}\right)$. I know it fails for perverse sheaves in characteristic $p$, and these usually behave the same as $D$-modules. | |
| Mar 1, 2011 at 18:12 | comment | added | AFK | Couldn't find the preprint on the web (I tried the Department of Math server and the RIMS preprint server). | |
| Mar 1, 2011 at 2:02 | comment | added | Kevin McGerty | I don't know of a reference beyond the work of Saito that you know of. In one of their recent preprints "Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants" Kontsevich and Soibelman discuss the vanishing cycle functor, and note in Section 7.4 (page 97) that there is a Thom-Sebastiani theorem in the mixed Hodge module case referring to a paper of Saito "Thom-Sebastiani theorem for Hodge modules" which is listed as a 2010 Kyoto University preprint. | |
| Dec 13, 2009 at 13:05 | comment | added | Thomas Riepe | BTW, it would be interesting to see Deligne's original proof, which was apparently never published. (Reference for Delignes's proof is Demazure, Sem. Bourbaki no. 443, p.7; a similar proof technique: Scholl "Vanishing Cycles ...", Inventiones 124) | |
| Dec 12, 2009 at 19:42 | history | asked | AFK | CC BY-SA 2.5 |