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Author: William A. Stein
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% $Header: /home/was/papers/thesis/RCS/thesis.tex,v 1.9 2000/05/15 04:42:54 was Exp $
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% thesis.tex: Ph.D. thesis %
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% Copyright (c) 2000 by William A. Stein, %
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% Department of Mathematics %
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% University of California, Berkeley %
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% [email protected] %
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% latex thesis
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% bibtex thesis
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% latex thesis
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% latex thesis
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% makeindex thesis.idx
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% latex thesis
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%
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% latex thesis;bibtex thesis;latex thesis;latex thesis;makeindex thesis.idx;latex thesis
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%\documentclass[twoside,draft]{ucthesis}
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\documentclass[twoside]{ucthesis}
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%\documentclass{ucthesis}
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\voffset = 0.59375in
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\hoffset = -1mm
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%\hoffset=-.75mm
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\usepackage{makeidx}
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\makeindex
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\usepackage[all]{xy}
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\usepackage{graphicx}
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\include{tmacros}
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\newcommand{\thetitle}{Explicit approaches to modular abelian varieties}
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%\includeonly{bsd}
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%\includeonly{modsyms}
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%\includeonly{bsd, algorithms}
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%\includeonly{algorithms}
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%\includeonly{compgroup}
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\begin{document}
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\ssp % remove for standard double-spaced thesis.
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\parindent=2em
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\CompileMatrices\UseTips
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\title{\thetitle}
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\author{William Arthur Stein}
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\degreesemester{Spring}
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\degreeyear{2000}
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\degree{Doctor of Philosophy}
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\chair{Professor Hendrik Lenstra}
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\othermembers{Professor Bjorn Poonen\\
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Professor Bin Yu}
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\numberofmembers{3}
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\prevdegrees{B.S. (Northern Arizona University) 1994}
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\field{Mathematics}
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\campus{Berkeley}
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\maketitle
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\approvalpage
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\copyrightpage
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\include{abstract}
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\begin{frontmatter}
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\addtocounter{page}{-2}
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\begin{dedication}
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\null\vfil
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{\large
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\begin{center}
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To my parents and my grandmother, Annette Maurer.
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%To those who inspired me: Kevin Buzzard,
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%Robert Coleman, Hendrik Lenstra, Barry Mazur,
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%Lo\"\i{}c Merel, Ken Ribet, and my family.\\\vspace{12pt}
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\end{center}}
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\vfil\null
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\end{dedication}
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\tableofcontents
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\listoffigures
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\listoftables
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\include{symbols}
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\begin{acknowledgements}
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It is a pleasure to thank my thesis adviser, Hendrik Lenstra, for
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patiently guiding my intellectual development in innumerable ways. In
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addition, Robert Coleman, Barry Mazur, and Ken Ribet generously shared
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their countless ideas and unbounded enthusiasm with me. Robert helped
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me to understand $p$-adics, Barry taught me to visualize
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Shafarevich-Tate groups, and Ken explained congruences, component
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groups, and tutored me in the elusive art of mathematical exposition.
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This thesis would not have been possible without the questions that
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arose out of exhilarating collaborations with Amod Agashe, Kevin Buzzard,
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Lo\"\i{}c Merel, David Moulton, Ed Schaefer, Helena Verrill, and Joe
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Wetherell. I would like to thank Ahmed Abbes, Matt Baker, Brian
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Conrad, J\'anos Csirik, Jordan Ellenberg, Edray Goins, David Jones,
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Ezra Miller, Bjorn Poonen, and Mak Trifkovic for asking and answering
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many stimulating questions.
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I wish to thank Hendrik Lenstra and Ken Ribet for providing
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me with financial support during part of the writing of this thesis,
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Sarah M.~Hallam for providing further support, the {\tt
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Cal@SiliconValley} university fellowship for supporting me throughout
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my final year, and the \magma{} group for their computational support.
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Finally, I would like to thank Bjorn Poonen for thoroughly reading this
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thesis and pointing out many ways in which it could be improved.
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\end{acknowledgements}
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\end{frontmatter}
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\pagestyle{headings}
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\setcounter{page}{1}
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% Preface
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\include{preface}
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% Chapter 1
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\include{bsd}
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% Chapter 2
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\include{modsyms}
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% Chapter 3
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\include{algorithms}
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% Chapter 4
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\include{compgroup}
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\bibliographystyle{amsplain}
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\bibliography{biblio}
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\printindex
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\end{document}
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