This is TeX, Version 3.14159 (Web2C 7.3.1) (format=tex 2000.7.19)  15 OCT 2000 00:31
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l.3 \comment
            {
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! Missing $ inserted.
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l.12 Changed F_
               p to F_v in proof of main theorem!
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                   \par 
l.13 
     
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! Missing $ inserted.
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                   _
l.21 got rid of a_
                  p
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                   \par 
l.22 
     
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
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                   _
l.30 quick fix. a_
                  p typo
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l.31 
     
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l.42 added\index
                {Mazur}
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! Undefined control sequence.
l.45 eliminated \index
                      {toric reduction}
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l.74 \chapter
             {The Birch and Swinnerton-Dyer conjecture}
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l.75 \label
           {chap:bsd}\index{Birch and Swinnerton-Dyer conjecture|see{BSD con...
The control sequence at the end of the top line
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l.75 \label{chap:bsd}\index
                           {Birch and Swinnerton-Dyer conjecture|see{BSD con...
The control sequence at the end of the top line
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misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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l.76 \index
           {Conjecture!Birch and Swinnerton-Dyer|see{BSD conjecture}}%
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spelling (e.g., `I\hbox'). Otherwise just continue,
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l.78 \index
           {Shimura-Taniyama conjecture}\index{Conjecture!Shimura and Taniyama}
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of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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l.78 \index{Shimura-Taniyama conjecture}\index
                                              {Conjecture!Shimura and Taniyama}
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misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
l.82 (see~\cite
               [pg.~549]{darmon-bsd} and \cite[Intro.]{cime-1997}).
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misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
l.82 (see~\cite[pg.~549]{darmon-bsd} and \cite
                                              [Intro.]{cime-1997}).
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l.86 conjecture\index
                     {BSD conjecture!is still unknown} is
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l.89 curves of analytic rank~$0$ (see~\cite
                                           {rubin:main-conjectures}), and
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l.91 the last twenty years (see, e.g.,~\cite
                                            {gross-zagier} and
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l.92 \cite
          {kolyvagin:mordellweil}).
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Overfull \hbox (14.1337pt too wide) in paragraph at lines 74--93
\tenrm con-jec-ture-Con-jec-ture!Birch and Swinnerton-Dyer|seeBSD con-jec-tureN
ow that the Shimura-TaniyamaShimura-|

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! Undefined control sequence.
l.94 Approaches to the BSD conjecture\index
                                           {BSD conjecture}
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l.95 that rely on congruences between\index
                                           {Congruences!and BSD conjecture}
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! Undefined control sequence.
l.96 modular forms\index
                        {Modular forms!and BSD}
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l.98 ...f the analogue of the BSD conjecture\index
                                                  {BSD conjecture!in higher ...
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l.104 ... thesis which cover similar themes.\index
                                                  {Agashe}  The paper of
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l.105 Cremona and Mazur's~\cite
                               {cremona-mazur}\index{Mazur} paints a detailed
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l.105 ...na and Mazur's~\cite{cremona-mazur}\index
                                                  {Mazur} paints a detailed
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l.108 \index
            {Congruences!and BSD conjecture}
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of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
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Overfull \hbox (4.13455pt too wide) in paragraph at lines 103--109
[]\tenrm The reader is urged to also read A. Agashe's 2000 Berke-ley Ph.D. the-
sis which cover sim-i-lar themes.Agashe|

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l.110 \section
              {The BSD conjecture}\index{BSD conjecture|textit}
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l.110 \section{The BSD conjecture}\index
                                        {BSD conjecture|textit}
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l.111 By~\cite
              {breuil-conrad-diamond-taylor} we now know
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<recently read> \Q 
                   
l.112 that every elliptic curve over~$\Q
                                        $ is
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l.116 Let~$J_0(N)$ denote the Jacobian\index
                                            {Jacobian} of $X_0(N)$; this is ...
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l.119 The survey article~\cite
                              {diamond-im} is a good
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l.123 Following Mazur~\cite
                           {mazur:rational}\index{Mazur}, we make the follow...
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misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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l.123 Following Mazur~\cite{mazur:rational}\index
                                                 {Mazur}, we make the follow...
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l.124 \begin
            {definition}[Optimal quotient]\index{Optimal quotient|textit}
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l.124 \begin{definition}[Optimal quotient]\index
                                                {Optimal quotient|textit}
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l.125 An {\em
              optimal quotient} of $J_0(N)$ is a quotient~$A$ of
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misspelled it (e.g., `\hobx'), type `I' and the correct
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Overfull \hbox (22.57014pt too wide) in paragraph at lines 123--127
[]\tenrm Following Mazur mazur:rationalMazur, we make the fol-low-ing def-i-ni-
tion. def-i-ni-tion[Optimal quo-tient]Optimal|

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