About

This is my bachelor project supervised by Jesper Grodal.

It is on the Geometric Satake equivalence, attributed to Mirković and Vilonen.

This is a short note on how to construct the convolution product in an $\infty$-categorical setting.

If $\mathcal{X}$ is an $\infty$-topos and $A\in\operatorname{Grp}(\mathcal{X})$ is a group object acting on a monoid object $M\in\operatorname{Mon}(\mathcal{X})$ compatibly from both left and right, then $D(A\backslash M/A)$ is a monoidal category (here $D$ is a six-functor formalism). The key claim is that $A\backslash M/A$ is an algebra object in $\operatorname{Corr}(\mathcal{X})$.

This note is a written supplement to a talk I gave during the semniar-course TopTop, taught by Lars Hesselholt.

In this note we construct the solid six-functor formalism on schemes of finite type over $\operatorname{Spec}(\mathbf{Z})$. As an application, we show Serre duality. The key takeaway is that this reduces to the case of the affine line $\mathbb A^1_{\mathbb Z}$

This note is a written supplement to a talk I gave during the semniar-course TopTop, taught by Lars Hesselholt.

We expand on some of the arguments from Chapter 5 of Dustin Clausen's preprint.