de RhamWitt cohomology

General Introduction
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Search results
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Online References
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Paper References
Illusie: Complexe de de RhamWitt et cohomologie cristalline
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Definition
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Properties
I think de RhamWitt theory turns up in the case of BlochKato, see this MO answer of Cisinski.
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
Dmitry Kaledin (Steklov): HochschildWitt complex. Abstract: "de RhamWitt complex" of Deligne and Illusie is a functorial complex of sheaves WΩ(X) on a smooth algebraic variety X over a finite field, computing the cristalline cohomology of X. I am going to present a noncommutative generalization of this: even for a noncommutative ring A, one can define a functorial "HochschildWitt complex" with homology WHH(A); if A is commutative, then WHHi(A)=WΩi(X), X = Spec A (this is analogous to the isomorphism HHi(A)=Ωi(X) discovered by Hochschild, Kostant and Rosenberg). Moreover, the construction of the HochschildWitt complex is actually simpler than the DeligneIllusie construction, and it allows to clarify the structure of the de RhamWitt complex.
From Thomas: Christopher Davis, a former student of Kedlaya, now in the Bonn MPI, does apparently interesting things with "overconvergent de RhamWitt cohomology", e.g. a theme in Rogne's seminar this summer. The most readable source shall be Chris' pdh thesis and Kedlaya suggested me to read that (because they want to prove some comparison theorems with that), but apparently Chris does not want to distribute it. Perhaps you are curious about that too and get it. An alternative source could be his paper with Zink and Langer, but far less readable.
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