Timeline for can an nonzero IC sheaf have zero hypercohomology?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 19, 2012 at 23:02 | vote | accept | Vivek Shende | ||
| Nov 19, 2012 at 21:07 | comment | added | Ben Webster♦ | yes, I should have said "no trivial composition factors." Since we were just looking for one example, I can also just assume rank 1. | |
| Nov 19, 2012 at 21:06 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
added 22 characters in body
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| Nov 19, 2012 at 21:04 | comment | added | Geordie Williamson | @Ben: When you say "non-trivial monodromy" I guess you mean invariants = coinvariants = 0. Of course local systems with unipotent monodromy on $\mathbb{C}^*$ have cohomology. | |
| Nov 19, 2012 at 21:02 | comment | added | Geordie Williamson | More generally one can take any $X$ and a proper and generically finite map $f : X -> X$. Then $\mathbb{H}(f_*\mathbb{Q}_X) = H^*(X)$ and so every summand of $f_*\mathbb{Q}_X$ except for $\mathbb{Q}_X$ (an IC by the decomposition theorem) has vanishing cohomology. | |
| Nov 19, 2012 at 19:04 | history | answered | Ben Webster♦ | CC BY-SA 3.0 |