s21-algebra-1/2021_Algebra_I.tex

\documentclass[10pt,ngerman,a4paper, fancyfoot, git]{mkessler-script}

\course{Algebra I}
\lecturer{Prof.~Dr.~Jens Franke}
\author{Josia Pietsch}

\title{title}

\usepackage{algebra}

\begin{document}

\maketitle
\cleardoublepage

\tableofcontents
\cleardoublepage


\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 $\mathfrak{l}$).
\pagebreak


\section{Finiteness conditions}
\input{inputs/finiteness_conditions}

\section{The Nullstellensatz and the Zariski topology}
\input{inputs/nullstellensatz_and_zariski_topology}


% Lecture 11
\section{Projective spaces}
\input{inputs/projective_spaces}

% Lecture 13
\section{Varieties}
\input{inputs/varieties}

\end{document}