Timeline for Can homotopy colimits recover cohomology sheaves?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 16, 2019 at 2:23 | comment | added | Peter LeFanu Lumsdaine | Another way to see $H_0\mathcal{A}$ is not in the image of the pushforward is to check that it isn’t fixed by the operation “pull back, then push forward”. | |
| Dec 15, 2019 at 18:02 | vote | accept | Federico Barbacovi | ||
| Dec 15, 2019 at 18:01 | comment | added | Federico Barbacovi | I see, thank you! | |
| Dec 15, 2019 at 17:59 | comment | added | Denis Nardin | @Federico almost: $\mathcal{A}$-modules are nothing to do with $k[x^{\pm1},y^{\pm1}]$-modules. $H_0\mathcal{A}$ is not in the subcategory because it generates everything under homotopy colimits (and so if it were, the subcategory would be everything but it's not). | |
| Dec 15, 2019 at 17:55 | comment | added | Federico Barbacovi | Let me see if I understand you counterexample. You are saying that the subcategory generated by $\mathcal{A}$ is contained in the subcategory $Rj_{\ast} D_{qc}(\mathbb{A}^2_{k} \setminus \{0\})$. by fully faithfulness and colimit preservation. However, $H_0 \mathcal{A}$ is not in this larger subcategory because it is not a module over $k[x^{\pm 1}, y^{\pm 1}]$, right? | |
| Dec 15, 2019 at 17:43 | history | answered | Denis Nardin | CC BY-SA 4.0 |