The Stacks project

40.1 Introduction

This chapter is devoted to advanced topics on groupoid schemes. Even though the results are stated in terms of groupoid schemes, the reader should keep in mind the $2$-cartesian diagram

40.1.0.1
\begin{equation} \label{more-groupoids-equation-quotient-stack} \vcenter { \xymatrix{ R \ar[r] \ar[d] & U \ar[d] \\ U \ar[r] & [U/R] } } \end{equation}

where $[U/R]$ is the quotient stack, see Groupoids in Spaces, Remark 76.19.4. Many of the results are motivated by thinking about this diagram. See for example the beautiful paper [K-M] by Keel and Mori.


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