Timeline for Yoga of six functors for group representations?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2017 at 18:03 | vote | accept | Saal Hardali | ||
| Jun 8, 2023 at 14:58 | |||||
| Feb 2, 2017 at 18:39 | comment | added | Matthias Wendt | Yes, $\pi_\ast$ and $\pi^\ast$ exist in the unbounded setting. I'm not so sure about the exceptional functors. In a sense, having the exceptional induction $Ind_!$ only in the case of subgroup inclusions and not for arbitrary homomorphisms doesn't seem that much of a restriction - do we really need induction in more general cases? The exceptional functors probably exist whenever the groups involved have finite cohomological dimension (and I suppose there are enough interesting groups with that property). | |
| Feb 2, 2017 at 18:09 | comment | added | Saal Hardali | It seems to me like the story should be that $\pi_*$ and $\pi^*$ always exist in the unbounded derived category (once correctly defined as you say). Then $\pi_!$ and $\pi^!$ exist for certain good situation. Formally in an ideal situation (by brown representability) to get a $\pi^!$ the $\pi_*$ should preserve arbitrary coproducts and to get a $\pi_!$ the $\pi^*$ should preserve arbitrary products. Does it look to you something like this holds in this case? (at least for discrete groups). | |
| Feb 2, 2017 at 16:10 | vote | accept | Saal Hardali | ||
| Feb 2, 2017 at 17:52 | |||||
| Feb 1, 2017 at 18:22 | history | bounty ended | CommunityBot | ||
| Jan 25, 2017 at 10:06 | history | edited | Matthias Wendt | CC BY-SA 3.0 |
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| Jan 24, 2017 at 22:19 | history | edited | Matthias Wendt | CC BY-SA 3.0 |
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| Jan 24, 2017 at 19:50 | history | answered | Matthias Wendt | CC BY-SA 3.0 |