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I’ve been thinking a lot about degeneration of Hodge to de Rham spectral sequence lately. I checked out the page on the nlab about it. I saw that there was a link to Cartier operator but no page, so I created it.
This actually got me thinking. In some sense degeneration at $E_1$ is “intrinsic” to the derived category $D(X)$ (I just made that up based on what I wrote in the article). There is a naive way to try to prove that if $X$ and $Y$ are derived equivalent and if the SS degenerates for one, the other should too. I couldn’t see a way to make it work. Is there an obvious reason this should be true, or an obvious counterexample?
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