% $Header: /home/was/papers/thesis/RCS/thesis.tex,v 1.9 2000/05/15 04:42:54 was Exp $123%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%4% thesis.tex: Ph.D. thesis %5% Copyright (c) 2000 by William A. Stein, %6% Department of Mathematics %7% University of California, Berkeley %8% [email protected] %9% latex thesis10% bibtex thesis11% latex thesis12% latex thesis13% makeindex thesis.idx14% latex thesis15%16% latex thesis;bibtex thesis;latex thesis;latex thesis;makeindex thesis.idx;latex thesis17%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1819%\documentclass[twoside,draft]{ucthesis}20\documentclass[twoside]{ucthesis}21%\documentclass{ucthesis}2223\voffset = 0.59375in24\hoffset = -1mm25%\hoffset=-.75mm2627\usepackage{makeidx}28\makeindex29\usepackage[all]{xy}30\usepackage{graphicx}31\include{tmacros}32\newcommand{\thetitle}{Explicit approaches to modular abelian varieties}3334%\includeonly{bsd}3536%\includeonly{modsyms}37%\includeonly{bsd, algorithms}38%\includeonly{algorithms}39%\includeonly{compgroup}4041\begin{document}42\ssp % remove for standard double-spaced thesis.43\parindent=2em44\CompileMatrices\UseTips454647\title{\thetitle}48\author{William Arthur Stein}49\degreesemester{Spring}50\degreeyear{2000}51\degree{Doctor of Philosophy}52\chair{Professor Hendrik Lenstra}53\othermembers{Professor Bjorn Poonen\\54Professor Bin Yu}55\numberofmembers{3}56\prevdegrees{B.S. (Northern Arizona University) 1994}57\field{Mathematics}58\campus{Berkeley}5960\maketitle61\approvalpage62\copyrightpage6364\include{abstract}6566\begin{frontmatter}67\addtocounter{page}{-2}68\begin{dedication}69\null\vfil70{\large71\begin{center}72To my parents and my grandmother, Annette Maurer.73%To those who inspired me: Kevin Buzzard,74%Robert Coleman, Hendrik Lenstra, Barry Mazur,75%Lo\"\i{}c Merel, Ken Ribet, and my family.\\\vspace{12pt}76\end{center}}77\vfil\null78\end{dedication}7980\tableofcontents81\listoffigures82\listoftables83\include{symbols}8485\begin{acknowledgements}86It is a pleasure to thank my thesis adviser, Hendrik Lenstra, for87patiently guiding my intellectual development in innumerable ways. In88addition, Robert Coleman, Barry Mazur, and Ken Ribet generously shared89their countless ideas and unbounded enthusiasm with me. Robert helped90me to understand $p$-adics, Barry taught me to visualize91Shafarevich-Tate groups, and Ken explained congruences, component92groups, and tutored me in the elusive art of mathematical exposition.9394This thesis would not have been possible without the questions that95arose out of exhilarating collaborations with Amod Agashe, Kevin Buzzard,96Lo\"\i{}c Merel, David Moulton, Ed Schaefer, Helena Verrill, and Joe97Wetherell. I would like to thank Ahmed Abbes, Matt Baker, Brian98Conrad, J\'anos Csirik, Jordan Ellenberg, Edray Goins, David Jones,99Ezra Miller, Bjorn Poonen, and Mak Trifkovic for asking and answering100many stimulating questions.101102I wish to thank Hendrik Lenstra and Ken Ribet for providing103me with financial support during part of the writing of this thesis,104Sarah M.~Hallam for providing further support, the {\tt105Cal@SiliconValley} university fellowship for supporting me throughout106my final year, and the \magma{} group for their computational support.107108Finally, I would like to thank Bjorn Poonen for thoroughly reading this109thesis and pointing out many ways in which it could be improved.110\end{acknowledgements}111112113\end{frontmatter}114115\pagestyle{headings}116117\setcounter{page}{1}118% Preface119\include{preface}120% Chapter 1121\include{bsd}122% Chapter 2123\include{modsyms}124% Chapter 3125\include{algorithms}126% Chapter 4127\include{compgroup}128129\bibliographystyle{amsplain}130\bibliography{biblio}131132\printindex133134\end{document}135136137