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In the accepted answer to this question, it is shown that for a proper algebraic variety $X$ we have that $H^{r-i}(X, W\Omega^i)[1/p]$ has slopes from the interval $[i, i+1[$, so namely is isomorphic to $H^{r-i}(X, W\Omega^i)[1/p][-i][i]$, the shift of a Cartier module with slopes in $[0, 1[$, which is thus a Dieudonne module, and thus is the Dieudonne module of some formal group, say $G_{i, r}$. For example, if $i=0$, this is $H^r(X, W\Omega^0)=H^r(X, \mathcal{W})=H^r(X, \mathbb{D(G_m)})=\mathbb{D}(H^r(X, \mathbb{G}_m))$, which is just the Artin-Mazur formal group law associated to $X$. I was wondering if there is a similar interpretations of other laws?

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