\begin{warning}
    This is not an official script!
    This document was written in preparation for the oral exam.
    It mostly follows the way \textsc{Prof.
        Franke} presented the material in his
    lecture rather closely.
    There are probably errors.
\end{warning}

\noindent The \LaTeX template by \textsc{Maximilian Kessler} is published under the
MIT-License and can be obtained from \url{https://github.com/kesslermaximilian/LatexPackages}.
% TODO
\newline

\noindent $\mathfrak{k}$ is {\color{red} always} an
algebraically closed field and $\mathfrak{k}^n$ is equipped with the
Zariski-topology.
Fields which are not assumed to be algebraically closed have been renamed
(usually to $\mathfrak{l}$).