Paper XII: Patching Support, Hecke Packets, and Conditional Automorphic Completion

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1 \begin{tikzpicture}[x=1cm,y=1cm,font=\small,>=Stealth]
2 
3 \node[font=\sffamily\bfseries] at (1.5,3.1) {modulo $25$};
4 \node[font=\sffamily\bfseries] at (8.5,3.1) {modulo $5$};
5 \node (A) at (1.5,2.1) {$\begin{pmatrix}1&23\\0&24\end{pmatrix}$};
6 \node (B) at (8.5,2.1) {$\begin{pmatrix}1&3\\0&4\end{pmatrix}\ne\begin{pmatrix}1&0\\0&4\end{pmatrix}$};
7 \draw[->] (A)--(B) node[midway,above,font=\footnotesize] {reduction};
8 \node[anchor=west,font=\footnotesize] at (0,1.1) {same conjugacy class; incompatible chosen matrices};
9 \node (D) at (1.5,0) {$\begin{pmatrix}1&0\\0&24\end{pmatrix}$};
10 \node (E) at (8.5,0) {$\begin{pmatrix}1&0\\0&4\end{pmatrix}$};
11 \draw[->] (D)--(E) node[midway,above,font=\footnotesize] {reduction};
12 \node[anchor=west,font=\footnotesize] at (0,-.9) {strictly compatible representatives};
13 
14 \end{tikzpicture}

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