Prismatic and $q$-crystalline sites of higher level
Algebraic Geometry
2022-05-17 v2 Number Theory
Abstract
In this article, we define the -prismatic site and the --crystalline site, which are higher level analogs of the prismatic site and the -crystalline site respectively. We prove a certain equivalence between the category of crystals on the -prismatic site (resp. the --crystalline site) and that on the prismatic site (resp. the -crystalline site), which can be regarded as the prismatic (resp. the -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 -prismatic site and that on the --crystalline site.
Keywords
Cite
@article{arxiv.2102.08151,
title = {Prismatic and $q$-crystalline sites of higher level},
author = {Kimihiko Li},
journal= {arXiv preprint arXiv:2102.08151},
year = {2022}
}
Comments
v2: update, 56 pages