diff --git a/lec.pdf b/lec.pdf
index 9021728..9e5ed4b 100644
Binary files a/lec.pdf and b/lec.pdf differ
diff --git a/lec02.tex b/lec02.tex
index a6a633d..d33d33f 100644
--- a/lec02.tex
+++ b/lec02.tex
@@ -19,7 +19,7 @@ Let $k$ be a field.
 \end{bsp}
 
 \begin{satz}[]
-    For a $k$-scheme $X$ the following are equvialent:
+    For a $k$-scheme $X$ the following are equivalent:
     \begin{enumerate}[(i)]
         \item $X$ is geometrically reduced
         \item for every reduced $k$-scheme $Y$, the fibre product $X \times_k Y$ is reduced.