Twisted differential operators and $q$-crystals
Algebraic Geometry
2022-03-16 v4
Abstract
We discuss the notion of a q-PD-envelope considered by Bhatt and Scholze in their recent theory of q-crystalline cohomology and explain the relation with our notion of a divided polynomial twisted algebra. Together with an interpretation of crystals on the q-crystalline site, that we call q-crystals, as modules endowed with some kind of stratification, it allows us to associate a module on the ring of twisted differential operators to any q-crystal. For simplicity, we explain here only the one dimensional case.
Cite
@article{arxiv.2004.14320,
title = {Twisted differential operators and $q$-crystals},
author = {Michel Gros and Bernard Le Stum and Adolfo Quirós},
journal= {arXiv preprint arXiv:2004.14320},
year = {2022}
}