Timeline for The derived category of $p$-complete abelian groups is comonadic over the derived category of $\mathbb F_p$-vector spaces?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 31 at 19:32 | vote | accept | Tim Campion | ||
| Sep 19 at 21:11 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 20 at 17:35 | answer | added | Brendan Murphy | timeline score: 3 | |
| Oct 6, 2023 at 13:46 | comment | added | Tyler Lawson | @TimCampion The mod-$p$ functor is given by tensoring with $\Bbb F_p$, equivalent to the perfect complex $\Bbb Z \to \Bbb Z$ in degrees 0 and 1. This complex is dualizable with dual $\Bbb F_p[-1]$, and so $\Bbb F_p \otimes M \simeq map(\Bbb F_p[-1], M)$. This makes the left adjoint tensoring with $\Bbb F_p[-1] = map(\Bbb F_p, \Bbb Z)$. | |
| Sep 30, 2023 at 7:34 | comment | added | Drew Heard | Theorem 2.30 (and its proof) of arxiv.org/pdf/1507.06869.pdf are relevant | |
| Sep 29, 2023 at 21:26 | comment | added | Z. M | The mod p functor is a finite colimit (the cofiber of multiplication by p), thus preserves (co)limits. | |
| Sep 29, 2023 at 20:52 | comment | added | LSpice |
TeX note: ${}^\to_\leftarrow$ {}^\to_\leftarrow is available without any need for tricky constructs as $\rightleftarrows$ \rightleftarrows. I edited accordingly.
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| Sep 29, 2023 at 20:52 | history | edited | LSpice | CC BY-SA 4.0 |
Oops, switched the arrows
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| Sep 29, 2023 at 20:36 | history | edited | LSpice | CC BY-SA 4.0 |
TeX; titles of papers
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| Sep 29, 2023 at 19:57 | history | edited | Tim Campion | CC BY-SA 4.0 |
deleted 36 characters in body
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| Sep 29, 2023 at 19:53 | comment | added | Tim Campion | Why does the mod p functor preserve limits? What is its left adjoint? | |
| Sep 29, 2023 at 19:06 | comment | added | Marc Hoyois | I agree with Z. M. Moreover, the mod $p$ functor preserves both limits and colimits, so it is both monadic and comonadic. | |
| Sep 29, 2023 at 19:04 | comment | added | Z. M | I think that this is a direct consequence of Beck's monadicity theorem (or more precisely, Lurie's generalization): the mod p functor is a left adjoint, conservative, and preserves totalizations of cosimplicial objects. | |
| Sep 29, 2023 at 18:45 | history | asked | Tim Campion | CC BY-SA 4.0 |