English

Prismatic and $q$-crystalline sites of higher level

Algebraic Geometry 2022-05-17 v2 Number Theory

Abstract

In this article, we define the mm-prismatic site and the mm-qq-crystalline site, which are higher level analogs of the prismatic site and the qq-crystalline site respectively. We prove a certain equivalence between the category of crystals on the mm-prismatic site (resp. the mm-qq-crystalline site) and that on the prismatic site (resp. the qq-crystalline site), which can be regarded as the prismatic (resp. the qq-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 mm-prismatic site and that on the (m1)(m-1)-qq-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