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Prismatic cohomology and de Rham-Witt forms

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Semen Molokov

Algebraic Geometry · Submitted 11 Aug 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Subsequently, we define a canonical map from de Rham-Witt forms to prismatic cohomology in the perfect case and prove that it is an isomorphism.

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arXiv ID2008.04956 (version 3)
Pith IDM3TY5T3N, Pith's permanent record of this paper and its review
CitationSemen Molokov. "Prismatic cohomology and de Rham-Witt forms." arXiv:2008.04956 (2020). https://pith.science/paper/M3TY5T3N
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,995 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.36 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; .

For any prism $(A, d)$, we construct an analogue of Fontaine's map $W_r(A/d) \to A/d\phi(d)\cdots\phi^{r-1}(d)$. Subsequently, we define a canonical map from de Rham-Witt forms to 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 for a $p$-completed polynomial algebra over $A/d$.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 For any prism $(A, d)$, we construct an analogue of Fontaine's map $W_r(A/d) \to A/d\phi(d)\cdots\phi^{r-1}(d)$. contribution 0.94 0.95 0.09 asserted 1.00
s1 Subsequently, we define a canonical map from de Rham-Witt forms to prismatic cohomology in the perfect case and prove that it is an isomorphism. contribution 0.51 0.96 0.59 asserted 1.00
s2 Using this result, we obtain an explicit description of the prismatic cohomology for a $p$-completed polynomial algebra over $A/d$. result 0.97 0.95 0.23 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

For any prism $(A, d)$, we construct an analogue of Fontaine's map $W_r(A/d) \to A/d\phi(d)\cdots\phi^{r-1}(d)$. Subsequently, we define a canonical map from de Rham-Witt forms to 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 for a $p$-completed polynomial algebra over $A/d$.

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