Abstract:
For an arbitrary prism $(A, d)$ we construct an analogue of Fontaine's map $W_r(A/d) \to A/d\phi(d)\cdots\phi^{r-1}(d)$. Then we define a canonical map from the de Rham–Witt forms to the prismatic cohomology in the perfect case and prove that it is an isomorphism. Using this result, we obtain an explicit description of the prismatic cohomology $H^i((S/A)_\Delta,\mathcal{O}_\Delta/d\phi(d)\cdots\phi^{n-1}(d))$, where $S$ is the $p$-completion of a polynomial algebra over $A/d$.
Bibliography: 16 titles.
Keywords:prisms, prismatic cohomology, Witt vectors, de Rham–Witt forms.
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