Rigid categories and Berkovich motives
Date:
In the summer semester ‘25, the HIOB was organized by Tess Bouis, Niklas Kipp, and Sebastian Wolf. The topic was the recent construction of Berkovich motives developed by Scholze in this paper. You can also find here the program of the seminar.
The goal of my talk was to prove that for a sufficiently nice arc-sheaf $X$ the $\inf$-category $D_{mot}(X)$ of motivic sheaves over $X$ is rigid over spectra. To do that, I gave a rapid overview of rigid $\inf$-categories and how they generalize rigidly-compactly generated categories. You can find my notes here.