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arXiv · 2403.11676

Prismatic crystals and $q$-Higgs fields

Takeshi Tsuji
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Abstract

Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a $q$-Higgs module and the associated $q$-Higgs complex on the bounded prismatic envelope of an embedding into a framed smooth algebra, when the base bounded prism is defined over the $q$-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.

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Takeshi Tsuji. 2024-03-18. Prismatic crystals and $q$-Higgs fields. https://arxiv.org/abs/2403.11676

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