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[anchor=east] at (-.3,2.25) {point $a$};
4 \node[anchor=east] at (-.3,1.4) {$\dim H^0(C_a)$};
5 \node[anchor=east] at (-.3,.55) {$\dim H^1(C_a)$};
6 \foreach \x/\a in {0/-2,1.5/-1,3/0,4.5/1,6/2}{
7 \node at (\x+.4,2.25) {$\a$};
8 \draw[black!35] (\x,1.05) rectangle ++(.8,.7);\draw[black!35] (\x,.2) rectangle ++(.8,.7);
9 }
10 \foreach \x in {0,1.5,4.5,6}{\node[text=black!45] at (\x+.4,1.4) {$0$};\node[text=black!45] at (\x+.4,.55) {$0$};}
11 \fill[black!12] (3,1.05) rectangle ++(.8,.7);\fill[black!12] (3,.2) rectangle ++(.8,.7);
12 \node at (3.4,1.4) {$1$};\node at (3.4,.55) {$1$};
13 \draw[decorate,decoration={brace,mirror,amplitude=4pt}] (3,-.05)--(3.8,-.05);
14 \node[anchor=north,font=\footnotesize] at (3.4,-.27) {the zero differential creates two cohomology groups};
15 
16 \end{tikzpicture}

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