%%This is a standard LaTeX2e article document template. personal version 12/5/200%%
\documentclass[12pt,twoside,fullpage]{amsart}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%packages%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{latexsym}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{amstext}
\input Math632Macros.sty
\input xy %This is a package for doing commutative diagrams
\xyoption{all}

\begin{document}
\begin{problem}
Let $\phi : \sF \rightarrow \sG$ be a morphism of sheaves.
\begin{itemize}
\item[(a)]  Show that $\im \phi \cong \sF / \ker \phi$.
\item[(b)]  Show that $\coker \phi \cong \sG / \im \phi$.
\end{itemize}
\end{problem}
\begin{proof}
Insert proof here.
\end{proof}
You don't need to worry about numbering the problems, latex will automatically number them once we combine them.

\vskip 50pt


For your convenience, here are some symbols, placed in ``Math632Macros.sty'' that you might find useful.

\begin{itemize}
\item[(i)]  The structure sheaf of a variety $X$, $\OO_X$.
\item[(ii)]  A curly Hom used for sheaves, $\sHom$.
\item[(iii)]  The complex number, $\bC$.
\item[(iv)]  The spectrum of a ring, $\Spec R$.
\item[(v)]  The proj of a graded ring, $\Proj R$.
\item[(vi)]  The support of a sheaf $\sF$, $\Supp \sF$.
\item[(vii)]  The picard group of a variety, $\pic X$.
\item[(viii)]  The annihilator of a module $M$, $\Ann_R M$.
\end{itemize}

\end{document}
