$q$-de Rham complexes of higher level

Kimihiko Li

Published 2024-01-04Version 1

In this article, we construct two kinds of de Rham-like complexes which compute the cohomology of complete crystals on higher-level $q$-crystalline site, which was introduced in the previous article of the author. One complex is the $q$-analog of the higher de Rham complex constructed by Miyatani, and another complex is the $q$-analog of the jet complex constructed by Le Stum-Quir\'os. The complexes we constructed can also be regarded as the higher-level analogs of the $q$-de Rham complex.