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Topological cyclic homology
Recovering crystalline cohomology: 
Topological cyclic homology
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Prismatic cohomology
Take homotopy fixed points of the cyclotomic structure on \({\operatorname{THH}}\) to get \({\operatorname{TC}}\), Topological cyclic homology
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topological K theory
See HH and Topological cyclic homology, cyclotomic trace, coherent cohomoloy.
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K-Theory
The Lichtenbaum-Quillen conjectures related to etale cohomology, Kummer-Vandiver conjecture, relations to THH and TC.