Timeline for Tannaka reconstruction for homotopy types
Current License: CC BY-SA 4.0
4 events
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| Jun 28 at 13:13 | history | edited | Bugs Bunny | CC BY-SA 4.0 |
added 7 characters in body
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| Jun 27 at 16:17 | comment | added | David Ben-Zvi | In general for this to work you need some condition on a group (arising as $\pi_1(X)$) that will allow you to detect it from its category of R-linear representations. I'm not sure what's the most natural replacement in general (short of going full Yoneda and just thinking about sheaves of spaces on X, which is too tautological). | |
| Jun 27 at 16:16 | comment | added | David Ben-Zvi | A natural version of this question is to consider the symmetric monoidal $\infty$-category of local systems of R-modules (for suitable ring or ring spectrum R) on X, which is the counterpart to 𝑄𝐶(𝑋) in algebraic geometry (and close to your maps to Grassmannians). Then rational / p-adic homotopy theory a la Quillen-Sullivan/Mandell tells you you can recover X from this when it is simply-connected or more generally nilpotent (since cochains on X arise as the self-ext of the trivial local system - for X nilpotent that generates). See Lurie's DAG XIII or (hopefully) somewhere in SAG. | |
| Jun 27 at 8:00 | history | asked | Bugs Bunny | CC BY-SA 4.0 |