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This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=latex)
entering extended mode
(./latex_0ec16092a0b94545044e7bb31b5aa838c2d28218_p.tex
LaTeX2e <2014/05/01>
Babel <3.9l> and hyphenation patterns for 2 languages loaded.
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No file latex_0ec16092a0b94545044e7bb31b5aa838c2d28218_p.aux.

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l.7 \documentclass
                  [12pt]{article}

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l.8 \usepackage
               {amsmath, amsfonts, amssymb}

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l.14 \begin{document}
                     
[1]
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.21 The field $\QQ
                   _p$ of $p$-adic numbers, like the real field $\RR$, is an
! Undefined control sequence.
\RR ->\mathbb 
              {R}
l.21 ...$p$-adic numbers, like the real field $\RR
                                                  $, is an
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.24 ...a system that supports computation in $\QQ
                                                  _p$ must provide some
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.28 ...is amounts to working in the quotient $\QQ
                                                  _p / p^n \ZZ_p$
! Undefined control sequence.
\ZZ ->\mathbb 
              {Z}
l.28 ...o working in the quotient $\QQ_p / p^n \ZZ
                                                  _p$
[2]
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.94 Define $\QQ
                _p' = \QQ_p\cup\{\infty, *\}$.
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.94 Define $\QQ_p' = \QQ
                         _p\cup\{\infty, *\}$.
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.106 We say an element of $\QQ
                               _p$ is \emph{representable} if it
[3]
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.112 (\QQ
          _p')^k \to \QQ_p'$ be
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.112 (\QQ_p')^k \to \QQ
                        _p'$ be
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.125 ...tilde{f}(\#(n_1), \dots, \#(n_k)) \in \QQ
                                                  _p$
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.129 ...tilde{f}(\#(n_1), \dots, \#(n_k)) \in \QQ
                                                  _p$
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.133 ...tilde{f}(\#(n_1), \dots, \#(n_k)) \in \QQ
                                                  _p$

Overfull \hbox (5.126pt too wide) in paragraph at lines 133--138
[]\OT1/cmr/m/n/12 If $[](#(\OML/cmm/m/it/12 n[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/1
2 ; [] ; \OT1/cmr/m/n/12 #(\OML/cmm/m/it/12 n[]\OT1/cmr/m/n/12 )) \OMS/cmsy/m/n
/12 2 \OML/cmm/m/it/12 Q[]$ \OT1/cmr/m/n/12 and $\OMS/cmsy/m/n/12 ^^@\OT1/cmr/m
/n/12 2[] + 1 \OMS/cmsy/m/n/12 ^^T \OML/cmm/m/it/12 v[]\OT1/cmr/m/n/12 ([](#(\O
ML/cmm/m/it/12 n[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; [] ; \OT1/cmr/m/n/12 #(\O
ML/cmm/m/it/12 n[]\OT1/cmr/m/n/12 ))) \OMS/cmsy/m/n/12 ^^T
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.149 ...et} of $(n,d)$ consists of all $x \in \QQ
                                                  _p$ such that

Overfull \hbox (55.70853pt too wide) in paragraph at lines 146--151
\OT1/cmr/m/n/12 An \OT1/cmr/m/it/12 pFP in-ter-val \OT1/cmr/m/n/12 con-sists of
 a pair $(\OML/cmm/m/it/12 n; d\OT1/cmr/m/n/12 )$, where $\OML/cmm/m/it/12 n$ \
OT1/cmr/m/n/12 is a pFP, and $\OML/cmm/m/it/12 d \OMS/cmsy/m/n/12 2 f^^@1\OML/c
mm/m/it/12 ; \OT1/cmr/m/n/12 0\OML/cmm/m/it/12 ; [] ; m; \OT1/cmr/m/n/12 +\OMS/
cmsy/m/n/12 1g$\OT1/cmr/m/n/12 .
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.153 (\QQ
          _p')^m \to \QQ_p'$ be
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.153 (\QQ_p')^m \to \QQ
                        _p'$ be
! Undefined control sequence.
\QQ ->\mathbb 
              {Q}
l.172 ...ices to extend them to operations on $\QQ
                                                  _p'$
[4] [5] (./latex_0ec16092a0b94545044e7bb31b5aa838c2d28218_p.aux) )
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### semi simple group (level 1) entered at line 14 (\begingroup)
### bottom level
(see the transcript file for additional information)
Output written on latex_0ec16092a0b94545044e7bb31b5aa838c2d28218_p.dvi (5 pages
, 12736 bytes).
Transcript written on latex_0ec16092a0b94545044e7bb31b5aa838c2d28218_p.log.

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