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\small\bfseries] at (1.6,3.15) {$\operatorname{Spec}R$};
4 \draw[->,line width=1.1pt] (.1,2.1)--(1.6,.35);
5 \draw[->,dashed] (3.1,2.1)--(1.6,.35);
6 \fill (.1,2.1) circle (.09);\draw[fill=white] (3.1,2.1) circle (.09);\fill (1.6,.35) circle (.09);
7 \node[above=6pt] at (.1,2.1) {$(x)$};\node[above=6pt] at (3.1,2.1) {$(y)$};
8 \node[below=6pt] at (1.6,.35) {$(x,y)$};
9 \node[font=\footnotesize,align=center] at (1.6,-.7) {Filled points: support of $R/(x)$.\\Arrows: specialization of prime ideals.};
10 \node[font=\sffamily\small\bfseries] at (7.6,3.15) {$\operatorname{Spec}T$};
11 \draw[->,line width=1.1pt] (7.6,2.1)--(7.6,.35);\fill (7.6,2.1) circle (.09);\fill (7.6,.35) circle (.09);
12 \node[right=8pt] at (7.6,2.1) {$(0)$};\node[right=8pt] at (7.6,.35) {$(y)$};
13 \node[font=\footnotesize,align=center] at (7.6,-.7) {The quotient retains one generic point\\and the common closed point.};
14 
15 \end{tikzpicture}

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