The $q$-de Rham complex

Abstract: References: Lecture X of Bhatt's notes. For more details, see the Bhatt-Scholze paper.

In this talk, we define the q-de Rham complex, show that it is a q-deformation of the usual de Rham complex, and state a conjecture about the coordinate independence of this construction (to be proved next lecture using q-crystalline cohomology).

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.