Timeline for Local cohomology with coefficients in ideals of parameters
Current License: CC BY-SA 4.0
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| Feb 22, 2023 at 18:21 | comment | added | Marc Besson | You're certainly right about H^1 being nontrivial if I is principal; I forgot to mention that. However I'm really interested about the 'internal structure' so to speak: the cohomology H^i when i is less than the number of generators. Thank you for your reference though! | |
| Feb 22, 2023 at 17:57 | comment | added | Karl Schwede | I'm not sure I believe in general that $H_I^1(\mathbb{A}^n, M) = 0$ if $I \not\subseteq M$. If $I$ happens to be principal say $I = (x_1)$, then that local cohomology should be nonzero no matter what. I expect that questions in this direction (D-module generators in this particularly combinatorial / toric setting) are well known but I don't know the literature well enough to point out things off the top of my head. You may want to look at this paper by Lyubeznik: eudml.org/doc/144121 As well as the papers that cite it. It might lead you two someone who has done this before. | |
| Feb 22, 2023 at 6:53 | history | edited | YCor | CC BY-SA 4.0 |
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| Feb 22, 2023 at 5:33 | history | asked | Marc Besson | CC BY-SA 4.0 |