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The Hodge-to-de Rham spectral sequence can be arbitrarily non-degenerate in positive characteristic
There is a long tradition of constructing smooth projective varieties in positive characteristic with non-degenerate Hodge-to-de Rham spectral sequences. In this paper, we show that for any $n\geq 1$ and any spot $(i, j)$ on the $E_n$-page, except for the cases where the differential is forced to be
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