Cohomology and Geometry of Deligne—Lusztig varieties for $\text{GL}_n$

In this talk, we give a brief overview of our study of the cohomology of the structure sheaf and canonical sheaf in the $\text{GL}_n$-case and the geometry of Deligne—Lusztig varieties and related structures. We will also explain how to obtain the compactly supported mod $p$-power cohomology groups of Deligne—Lusztig varieties from our result.