Timeline for Periodicity Theorem for D(R)
Current License: CC BY-SA 3.0
4 events
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| Nov 1, 2012 at 23:19 | comment | added | Jonathan Beardsley | And I'm not sure I agree that the periodicity theorem "comes from" that stratification. But if you can ascertain that, then you're right, we shouldn't have something analogous in rings necessarily, unless we can find a similar structure. | |
| Nov 1, 2012 at 23:18 | comment | added | Jonathan Beardsley | What I mean is, there are analogues of the Morava K-theories, which are basically the residue fields $k(\mathfrak{p})$. These things homology acyclics (use Tor), in a sensible way, and seem to give a sensible thick subcategory theorem. The question for me is, can I find a self-map $f$ of a perfect complex $X$ of type $\mathfrak{p}$ whose cofiber is type (and this isn't really defined) $\mathfrak{p}+1$, but I'd like it to be some kind of minimal deformation of $\mathfrak{p}$ or something. Whatever that means. And I would like for this to induce periodic families in $[R,R]$. | |
| Nov 1, 2012 at 23:14 | comment | added | Dylan Wilson | "isn't really a linear ordering of the primes" Exactly. The periodicity theorem comes from the stratification of the moduli stack of formal groups, in the case of spectra. For D(R) there isn't really an analog in general. It's not clear to me what such a "periodicity theorem" would even say, in this case... But I could just be silly! | |
| Nov 1, 2012 at 20:15 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |