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?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.