| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

4. Specific cases


    1. Add remark

      Problem 4.1.

      [Vera Serganova] Take the Verlinde category $Ver_p$ and consider $GL(X)$ for $X \in Ver_p$. Compute the cohomology of this group scheme or other finite group schemes in $Ver_p$.


        • Add remark

          Problem 4.2.

          [Antoine Touze] Let $\mathbf{k}$ be a Noetherian ring and $G$ a reductive group scheme over $\mathbf{k}$. Suppose that $G$ acts on a finitely generated $\mathbf{k}$-algebra $A$. Is $H^*(G, A)$ finitely generated?
          1. $\mathbf{Z}$ is a good ring to start with.
          2. This is known if $\mathbf{k}$ is a field, and also for $sl_2$ and $sl_3$.


            • Add remark

              Problem 4.3.

              [Hector Pena Pollastri] Compute the cohomology of Deligne interpolation categories $GL_t$ for $t \in \mathbf{Z}$.

                  Cite this as: AimPL: Finite tensor categories: their cohomology and geometry, available at http://aimpl.org/finitetensor.