Prismatic crystals and -Higgs fields
arXiv:2403.11676
Abstract
Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a -Higgs module and the associated -Higgs complex on the bounded prismatic envelope of an embedding into a framed smooth algebra, when the base bounded prism is defined over the -crystalline prism. We also discuss its behavior under the scalar extension by the Frobenius lifting and tensor products, and a global description of the cohomology of a prismatic crystal via Zariski cohomological descent.