\documentclass[12pt]{amsart}

\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amscd}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{enumerate}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{textcomp}
\usepackage{latexsym}
\usepackage[all]{xy}
\usepackage{mathrsfs}
\usepackage{oldgerm}
\usepackage{euscript}
\usepackage{graphicx}

\input xy
\xyoption{all}

\theoremstyle{plain}
\newtheorem{theo}{Theorem}[section]
\newtheorem{main}[theo]{Main Theorem (Ribet)}
\newtheorem{lem}[theo]{Lemma}
\newtheorem{cor}[theo]{Corollary}
\newtheorem{prop}[theo]{Proposition}
\newtheorem{theodefi}[theo]{Theorem and Definition}
\newtheorem{conj}[theo]{Conjecture}

\theoremstyle{remark}
\newtheorem{rem}[theo]{Remark}

\theoremstyle{definition}
\newtheorem{defi}[theo]{Definition}
\newtheorem{exs}[theo]{Examples}
\newtheorem{ex}[theo]{Example}
\newtheorem{nota}[theo]{Notation}
\newtheorem{para}[theo]{}

\newenvironment{pr}{\textsc{Proof}}{}
\newenvironment{Ex}{\textbf{Exercise}}{ }

\DeclareMathOperator{\FF}{\mathcal{F}}
\DeclareMathOperator{\HH}{\mathcal{H}}
\DeclareMathOperator{\Supp}{Supp}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\Ker}{Ker}

\def\N{\mathbb{N}}
\def\Z{\mathbb{Z}}
\def\R{\mathbb{R}}
\def\Q{\mathbb{Q}}
\def\C{\mathbb{C}}

\def\ds{\displaystyle}

\begin{document}

\title{Standard Template}
\author{Y.P. Lee's Class}
\maketitle

\begin{description}
