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arXiv · 2102.08151

Prismatic and $q$-crystalline sites of higher level

Kimihiko Li
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Abstract

In this article, we define the $m$-prismatic site and the $m$-$q$-crystalline site, which are higher level analogs of the prismatic site and the $q$-crystalline site respectively. We prove a certain equivalence between the category of crystals on the $m$-prismatic site (resp. the $m$-$q$-crystalline site) and that on the prismatic site (resp. the $q$-crystalline site), which can be regarded as the prismatic (resp. the $q$-crystalline) analog of the Frobenius descent due to Berthelot and the Cartier transform due to Ogus-Vologodsky, Oyama and Xu. We also prove the equivalence between the category of crystals on the $m$-prismatic site and that on the $(m-1)$-$q$-crystalline site.

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Kimihiko Li. 2021-02-16. Prismatic and $q$-crystalline sites of higher level. https://arxiv.org/abs/2102.08151

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