diff --git a/lec02.pdf b/lec02.pdf
index fe4e6bc..6fb70cd 100644
Binary files a/lec02.pdf and b/lec02.pdf differ
diff --git a/lec02.tex b/lec02.tex
index fc685a2..a6a633d 100644
--- a/lec02.tex
+++ b/lec02.tex
@@ -10,7 +10,7 @@ Let $k$ be a field.
     Let $\mathcal{P}$ be a property of schemes over fields. For
     a $k$-scheme $X$ we say
     \emph{$X$ is geometrically} $\mathcal{P}$ if for all field extensions
-    $K / k$ the base change $X_K \to \mathrm{Spec}\ K$ is $\mathcal{P}$.
+    $K / k$ the base change $X_K \to \Spec K$ is $\mathcal{P}$.
 \end{definition}
 
 \begin{bsp}
diff --git a/lecture.cls b/lecture.cls
index e604222..68f00be 100644
--- a/lecture.cls
+++ b/lecture.cls
@@ -183,6 +183,8 @@
 % people seem to prefer varepsilon over epsilon
 \renewcommand{\epsilon}{\varepsilon}
 
+\newcommand{\Spec}{\operatorname{Spec}}
+
 \ExplSyntaxOn
 
 % S-tackrelcompatible ALIGN environment