fix sectioning

2021_Algebra_I.tex

@@ -31,7 +31,7 @@ Fields which are not assumed to be algebraically closed have been renamed (usual
 \pagebreak
 
 
-\subsection{Finiteness conditions}
+\section{Finiteness conditions}
 
 \subsection{Finitely generated and Noetherian modules}
 
@@ -313,7 +313,7 @@ is injective. $n$ and the $a_i$ can be chosen such that $A$ is finite over the i
     This contradicts the minimality of $n$, as $B$ can be generated by $< n$ elements $b_i$.
 
 \end{proof}
-\subsection{The Nullstellensatz and the Zariski topology}
+\section{The Nullstellensatz and the Zariski topology}
 \subsection{The Nullstellensatz} %LECTURE 1
 Let $\mathfrak{k}$ be a field, $R \coloneqq \mathfrak{k}[X_1,\ldots,X_n], I \subseteq R$ an ideal.
 
@@ -1913,7 +1913,7 @@ $\rad(A) = f A$ where $f = \prod_{i=1}^{n} p_i$.
 
 % Lecture 11
 
-\subsection{Projective spaces}
+\section{Projective spaces}
 Let $\mathfrak{l}$ be any field.
 \begin{definition}
     For a $\mathfrak{l}$-vector space $V$, let $\mathbb{P}(V)$ be the set of one-dimensional subspaces of $V$.
@@ -2278,7 +2278,7 @@ If $P_e $ with $e < d$ was $\neq 0$, it could not be a multiple of $P$ contradic
 
 
 % Lecture 13
-\subsection{Varieties}
+\section{Varieties}
 
 \subsection{Sheaves}
 
@@ -2927,7 +2927,7 @@ Original (Noether normalization)
 Artin-Tate
 Uncountable fields
 \begin{landscape}
-\subsection{Übersicht}
+\section{Übersicht}
 {\rowcolors{2}{gray!10}{white}
     \begin{longtable}{lll}
   \end{longtable}

algebra.sty

@@ -14,8 +14,6 @@
 
 \RequirePackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
 
-\setlength{\droptitle}{-1.0cm}
-
 \RequirePackage[normalem]{ulem}
 \RequirePackage{pdflscape}
 \RequirePackage{longtable}