Timeline for What is a higher derived constructible sheaf
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2013 at 1:28 | comment | added | Sam Gunningham | The difference is more clear in the case $X = S^1$; in that case, the usual constructible derived category would decompose in to blocks for each generalized eigenvalue of the monodromy. This sees only the profinite completion of $\pi_1(S^1) = \mathbb Z$, as opposed to all representations. | |
| Apr 24, 2013 at 1:25 | comment | added | Sam Gunningham | @BZ: Good point. I think the answer should be yes in reasonable cases, but you have to be careful about what you mean by the constructible derived category. For example, a constructible sheaf is usually taken to have finite dimensional stalks. The issue occurs even with no stratification (i.e. local systems). If $X$ is simply connected with no stratification (say), then the I would say that the usual constructible derived category is equivalent to $C^\ast(X)$-mod. This is not (quite) the same as $C_\ast (\Omega X)$-modules (though the two are closely related. | |
| Apr 24, 2013 at 0:44 | comment | added | David Ben-Zvi | The exit path description is beautiful, and some version of it is necessary for an unstable version of the question, but I think for the question as asked just the usual dg enhancement of the constructible derived category will do..? | |
| Apr 23, 2013 at 23:54 | vote | accept | Dmitry Vaintrob | ||
| Apr 23, 2013 at 23:54 | comment | added | Dmitry Vaintrob | Thanks! This is great. Looking at Aaron Smith's website, I saw he's working on a paper with Block on a constructible Riemann-Hilbert correspondence. | |
| Apr 23, 2013 at 23:49 | vote | accept | Dmitry Vaintrob | ||
| Apr 23, 2013 at 23:50 | |||||
| Apr 23, 2013 at 22:58 | history | answered | Sam Gunningham | CC BY-SA 3.0 |