CoCalc Public Fileswww / papers / thesis-old / tmacros.texOpen with one click!
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
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% macros.tex
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{amsthm}
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\newcommand{\subsubsubsection}[1]{\par\noindent{\em #1}\hspace{1em}}
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\author{William A. Stein\footnote{University of California, Berkeley, U.S.A.,
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{\tt was@math.berkeley.edu}}}
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\font\cyr=wncyr10 scaled \magstep 1
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\newcommand{\fpqf}{fpqf}
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\newcommand{\ccdot}{\!\cdot\!}
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\newcommand{\abvar}[1]{\mbox{\rm #1}}
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\newcommand{\twopii}{2\pi{}i{}}
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\newcommand{\Adual}{A^{\vee}}
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\newcommand{\Jdual}{J^{\vee}}
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\newcommand{\sM}{\boldsymbol{\mathcal{M}}}
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\newcommand{\esM}{\overline{\sM}}
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\newcommand{\sE}{\boldsymbol{\mathcal{E}}}
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\newcommand{\sS}{\boldsymbol{\mathcal{S}}}
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\newcommand{\sB}{\boldsymbol{\mathcal{B}}}
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\newcommand{\sMdual}{\widehat{\sM}}
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\newcommand{\sSdual}{\widehat{\sS}}
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\newcommand{\sMdualnew}{\widehat{\boldsymbol{\mathcal{M}}}^{\new}}
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\newcommand{\sSdualnew}{\widehat{\boldsymbol{\mathcal{S}}}^{\new}}
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\newcommand{\zbar}{\overline{z}}
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\newcommand{\corrto}{\longleftrightarrow}
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\newcommand{\eE}{\mathcal{E}}
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\newcommand{\msym}[3]{\langle #1, (#2, #3)\rangle}
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\newcommand{\defn}[1]{{\em #1}}
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\newcommand{\solution}[1]{\vspace{1em}%
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\par\noindent{\bf Solution #1.} }
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\newcommand{\todo}[1]{\noindent$\bullet$ {\small \textsf{#1}} $\bullet$\\}
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\newcommand{\done}[1]{\noindent {\small \textsf{Done: #1}}\\}
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\newcommand{\danger}[1]{\marginpar{\small \textsl{#1}}}
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\newcommand{\oo}{\infty}
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\DeclareMathOperator{\Reg}{Reg}
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\DeclareMathOperator{\an}{an}
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\DeclareMathOperator{\lcm}{lcm}
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\DeclareMathOperator{\cores}{cores}
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\DeclareMathOperator{\coker}{coker}
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%\DeclareMathOperator{\Re}{Re}
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\newcommand{\define}{:=}
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%\newcommand{\defeq}{\stackrel{\mbox{\tiny def}}{=}}
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\newcommand{\defeq}{:=}
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\newcommand{\isog}{\simeq}
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\newcommand{\e}{\mathbf{e}}
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\newcommand{\bN}{\mathbf{N}}
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\newcommand{\Sha}{\mbox{\cyr X}}
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\newcommand{\Shaan}{\Sha_{\mbox{\tiny \rm an}}}
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\newcommand{\TS}{Tate-Shafarevich group}
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\newcommand{\Gam}{\Gamma}
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\newcommand{\gzero}{\Gamma_0(N)}
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\newcommand{\gone}{\Gamma_1(N)}
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\newcommand{\gam}{\gamma}
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\renewcommand{\Im}{\text{Im}}
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\newcommand{\X}{\mathcal{X}}
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\newcommand{\bA}{\mathbf{A}}
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\newcommand{\cH}{\mathcal{H}}
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\newcommand{\cP}{\mathcal{P}}
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\newcommand{\cA}{\mathcal{A}}
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\newcommand{\M}{\mathcal{M}}
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\newcommand{\cF}{\mathcal{F}}
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\newcommand{\cG}{\mathcal{G}}
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\DeclareMathOperator{\Jac}{Jac}
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\DeclareMathOperator{\Ker}{Ker}
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\DeclareMathOperator{\sign}{sign}
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\DeclareMathOperator{\unr}{unr}
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\newcommand{\N}{\mathcal{N}}
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\newcommand{\U}{\mathcal{U}}
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\newcommand{\Kbar}{\overline{K}}
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\newcommand{\Lbar}{\overline{L}}
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\newcommand{\gammabar}{\overline{\gamma}}
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\newcommand{\q}{\mathbf{q}}
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\renewcommand{\star}{\times}
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\newcommand{\gM}{\mathfrak{M}}
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\newcommand{\gA}{\mathfrak{A}}
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\newcommand{\gP}{\mathfrak{P}}
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\newcommand{\bmu}{\boldsymbol{\mu}}
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\newcommand{\union}{\cup}
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\newcommand{\Tl}{T_{\ell}}
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\newcommand{\con}{\equiv}
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\newcommand{\set}[1]{\{#1\}}
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\newcommand{\iv}{^{-1}}
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\newcommand{\alp}{\alpha}
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\newcommand{\bq}{\mathbf{q}}
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\newcommand{\hecke}{{\sc Hecke}}
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\newcommand{\lidia}{{\tt LiDIA}}
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\newcommand{\cpp}{{\tt C++}}
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\newcommand{\tensor}{\otimes}
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\newcommand{\bg}{{\tt BruceGenus}}
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\newcommand{\abcd}[4]{\left(
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\begin{smallmatrix}#1&#2\\#3&#4\end{smallmatrix}\right)}
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\begin{matrix}#1&#2&#3\\#4&#5&#6\\#7&#8&#9
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\end{matrix}\right)}
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\begin{matrix}#1&#2\\#3&#4
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\end{matrix}\right)}
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\begin{matrix}#1\\#2
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\end{matrix}\right)}
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\newcommand{\smallvtwo}[2]{\left(
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\begin{smallmatrix}#1\\#2
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\end{smallmatrix}\right)}
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\newcommand{\smallmtwo}[4]{\left(
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\begin{smallmatrix}#1&#2\\#3&#4
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\end{smallmatrix}\right)}
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\newcommand{\eps}{\varepsilon}
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\newcommand{\vphi}{\varphi}
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\newcommand{\gp}{\mathfrak{p}}
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\newcommand{\W}{\mathcal{W}}
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\newcommand{\oz}{\overline{z}}
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\newcommand{\Zpstar}{\Zp^{\star}}
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\newcommand{\Zhat}{\widehat{\Z}}
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\newcommand{\comment}[1]{}
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\newcommand{\Q}{\mathbf{Q}}
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\newcommand{\GQ}{G_{\Q}}
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\newcommand{\R}{\mathbf{R}}
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\newcommand{\D}{{\mathbb D}}
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\newcommand{\cC}{\mathcal{C}}
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\newcommand{\cD}{\mathcal{D}}
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\newcommand{\cS}{\mathcal{S}}
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\newcommand{\Sbar}{\overline{S}}
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\newcommand{\K}{{\mathbb K}}
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\newcommand{\C}{\mathbf{C}}
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\newcommand{\Cp}{{\mathbb C}_p}
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\newcommand{\Sets}{\mbox{\rm\bf Sets}}
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\newcommand{\bcC}{\boldsymbol{\mathcal{C}}}
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\renewcommand{\P}{\mathbf{P}}
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\newcommand{\Qbar}{\overline{\Q}}
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\newcommand{\Zbar}{\overline{\Z}}
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\newcommand{\kbar}{\overline{k}}
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\newcommand{\dual}{\bot}
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\newcommand{\T}{\mathbf{T}}
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\newcommand{\calT}{\mathcal{T}}
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\newcommand{\cT}{\mathcal{T}}
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\newcommand{\cbT}{\mathbf{\mathcal{T}}}
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\newcommand{\cU}{\mathcal{U}}
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\newcommand{\Z}{\mathbf{Z}}
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\newcommand{\Zl}{\mathbf{Z}_\ell}
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\newcommand{\F}{\mathbf{F}}
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\newcommand{\Fl}{\F_{\ell}}
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\newcommand{\Flbar}{\overline{\F}_{\ell}}
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\newcommand{\Flnu}{\F_{\ell^{\nu}}}
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\newcommand{\Fbar}{\overline{{\mathbb F}}}
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\newcommand{\Fpbar}{\overline{\F}_p}
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\newcommand{\fbar}{\overline{f}}
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\newcommand{\Qp}{\Q_p}
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\newcommand{\Ql}{\Q_{\ell}}
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\newcommand{\Qlbar}{\overline{\Q}_{\ell}}
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\newcommand{\Qlnr}{\Q_{\ell}^{\text{nr}}}
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\newcommand{\Qltm}{\Q_{\ell}^{\text{tame}}}
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\newcommand{\Qv}{\Q_v}
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\newcommand{\Qpbar}{\Qbar_p}
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\newcommand{\Zp}{\Z_p}
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\newcommand{\Fp}{\F_p}
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\newcommand{\Fq}{\F_q}
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\newcommand{\Fqbar}{\overline{\F}_q}
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\newcommand{\Ad}{Ad}
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\newcommand{\adz}{\Ad^0}
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\renewcommand{\O}{\mathcal{O}}
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\newcommand{\A}{\mathcal{A}}
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\newcommand{\Og}{O_{\gamma}}
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\newcommand{\isom}{\cong}
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\newcommand{\ncisom}{\approx} % noncanonical isomorphism
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\newcommand{\almost}{\sim}
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\DeclareMathOperator{\Aut}{Aut}
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\DeclareMathOperator{\Frob}{Frob}
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\DeclareMathOperator{\Ver}{Ver}
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\DeclareMathOperator{\Norm}{Norm}
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\DeclareMathOperator{\ord}{ord}
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\DeclareMathOperator{\GL}{GL}
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\DeclareMathOperator{\PSL}{PSL}
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\DeclareMathOperator{\PGL}{PGL}
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\DeclareMathOperator{\Gal}{Gal}
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\DeclareMathOperator{\SO}{SO}
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\newcommand{\galq}{\Gal(\Qbar/\Q)}
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\newcommand{\cE}{\mathcal{E}}
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\newcommand{\cR}{\mathcal{R}}
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\newcommand{\cX}{\mathcal{X}}
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\newcommand{\sltwoz}{\SL_2(\Z)}
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\newcommand{\sltwo}{\SL_2}
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\newcommand{\gltwoz}{\GL_2(\Z)}
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\newcommand{\mtwoz}{M_2(\Z)}
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\newcommand{\gltwoq}{\GL_2(\Q)}
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\newcommand{\gltwo}{\GL_2}
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\newcommand{\gln}{\GL_n}
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\newcommand{\psltwoz}{\PSL_2(\Z)}
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\newcommand{\psltwo}{\PSL_2}
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\newcommand{\h}{\mathfrak{h}}
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\renewcommand{\a}{\mathfrak{a}}
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\newcommand{\p}{\mathfrak{p}}
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\newcommand{\m}{\mathfrak{m}}
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\newcommand{\trho}{\tilde{\rho}}
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\newcommand{\rhol}{\rho_{\ell}}
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\newcommand{\rhoss}{\rho^{\text{ss}}}
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\DeclareMathOperator{\tr}{tr}
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\DeclareMathOperator{\ur}{ur}
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\DeclareMathOperator{\Hom}{Hom}
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\DeclareMathOperator{\Ext}{Ext}
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\DeclareMathOperator{\Tor}{Tor}
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\newcommand{\smallzero}{\left(\begin{smallmatrix}0&0\\0&0
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\end{smallmatrix}\right)}
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\newcommand{\smallone}{\left(\begin{smallmatrix}1&0\\0&1
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\end{smallmatrix}\right)}
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\newcommand{\pari}{PARI}
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\newcommand{\magma}{{\sc Magma}}
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\newcommand{\ksep}{k^{\sep}}
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%%%% Theoremstyles
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\theoremstyle{plain}
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\newtheorem{theorem}{Theorem}[chapter]
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{conjecture}[theorem]{Conjecture}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{algorithm}[theorem]{Algorithm}
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\newtheorem{question}[theorem]{Question}
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\newtheorem{selfnote}[theorem]{Note that will be removed}
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\newtheorem{warning}[theorem]{WARNING}
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\theoremstyle{remark}
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\newtheorem{goal}[theorem]{Goal}
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\newtheorem{remark}[theorem]{Remark}
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\newtheorem{example}[theorem]{Example}
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\newtheorem{exercise}[theorem]{Exercise}
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% bulleted list environment
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\newenvironment{bulletlist}
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{
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\begin{list}
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{$\bullet$}
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{
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\setlength{\itemsep}{.5ex}
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\setlength{\parsep}{0ex}
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\setlength{\parskip}{0ex}
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\setlength{\topsep}{.5ex}
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}
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}
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{
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\end{list}
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}
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%end newenvironment
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% bulleted list environment
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\newenvironment{dashlist}
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{
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\begin{list}
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{---}
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{
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\setlength{\itemsep}{.5ex}
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\setlength{\parsep}{0ex}
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\setlength{\parskip}{0ex}
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\setlength{\topsep}{.5ex}
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}
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}
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{
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\end{list}
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}
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%end newenvironment
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% numbered list environment
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\newcounter{listnum}
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\newenvironment{numlist}
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{
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\begin{list}
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{{\em \thelistnum.}}{
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\usecounter{listnum}
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\setlength{\itemsep}{.5ex}
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\setlength{\parsep}{0ex}
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\setlength{\parskip}{0ex}
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\setlength{\topsep}{.5ex}
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}
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}
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{
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\end{list}
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}
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%end newenvironment
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