s21-algebra-1/2021_Algebra_I.tex

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\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}