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% thesis.tex: Ph.D. thesis %
% Copyright (c) 2000 by William A. Stein, %
% Department of Mathematics %
% University of California, Berkeley %
% was@math.berkeley.edu %
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%\documentclass[twoside,draft]{ucthesis}
\documentclass[twoside]{ucthesis}
%\documentclass{ucthesis}
\voffset = 0.59375in
\hoffset = -1mm
%\hoffset=-.75mm
\usepackage{makeidx}
\makeindex
\usepackage[all]{xy}
\usepackage{graphicx}
\include{tmacros}
\newcommand{\thetitle}{Explicit approaches to modular abelian varieties}
%\includeonly{bsd}
%\includeonly{modsyms}
%\includeonly{bsd, algorithms}
%\includeonly{algorithms}
%\includeonly{compgroup}
\begin{document}
\ssp % remove for standard double-spaced thesis.
\parindent=2em
\CompileMatrices\UseTips
\title{\thetitle}
\author{William Arthur Stein}
\degreesemester{Spring}
\degreeyear{2000}
\degree{Doctor of Philosophy}
\chair{Professor Hendrik Lenstra}
\othermembers{Professor Bjorn Poonen\\
Professor Bin Yu}
\numberofmembers{3}
\prevdegrees{B.S. (Northern Arizona University) 1994}
\field{Mathematics}
\campus{Berkeley}
\maketitle
\approvalpage
\copyrightpage
\include{abstract}
\begin{frontmatter}
\addtocounter{page}{-2}
\begin{dedication}
\null\vfil
{\large
\begin{center}
To my parents and my grandmother, Annette Maurer.
%To those who inspired me: Kevin Buzzard,
%Robert Coleman, Hendrik Lenstra, Barry Mazur,
%Lo\"\i{}c Merel, Ken Ribet, and my family.\\\vspace{12pt}
\end{center}}
\vfil\null
\end{dedication}
\tableofcontents
\listoffigures
\listoftables
\include{symbols}
\begin{acknowledgements}
It is a pleasure to thank my thesis adviser, Hendrik Lenstra, for
patiently guiding my intellectual development in innumerable ways. In
addition, Robert Coleman, Barry Mazur, and Ken Ribet generously shared
their countless ideas and unbounded enthusiasm with me. Robert helped
me to understand $p$-adics, Barry taught me to visualize
Shafarevich-Tate groups, and Ken explained congruences, component
groups, and tutored me in the elusive art of mathematical exposition.
This thesis would not have been possible without the questions that
arose out of exhilarating collaborations with Amod Agashe, Kevin Buzzard,
Lo\"\i{}c Merel, David Moulton, Ed Schaefer, Helena Verrill, and Joe
Wetherell. I would like to thank Ahmed Abbes, Matt Baker, Brian
Conrad, J\'anos Csirik, Jordan Ellenberg, Edray Goins, David Jones,
Ezra Miller, Bjorn Poonen, and Mak Trifkovic for asking and answering
many stimulating questions.
I wish to thank Hendrik Lenstra and Ken Ribet for providing
me with financial support during part of the writing of this thesis,
Sarah M.~Hallam for providing further support, the {\tt
Cal@SiliconValley} university fellowship for supporting me throughout
my final year, and the \magma{} group for their computational support.
Finally, I would like to thank Bjorn Poonen for thoroughly reading this
thesis and pointing out many ways in which it could be improved.
\end{acknowledgements}
\end{frontmatter}
\pagestyle{headings}
\setcounter{page}{1}
% Preface
\include{preface}
% Chapter 1
\include{bsd}
% Chapter 2
\include{modsyms}
% Chapter 3
\include{algorithms}
% Chapter 4
\include{compgroup}
\bibliographystyle{amsplain}
\bibliography{biblio}
\printindex
\end{document}