\input amstex
\documentstyle{amsppt}
\mag=\magstep1

\document
\NoBlackBoxes
$$
\matrix
	\format \l & \l \\
	\matrix
		\format \l \\
		\noalign{\vskip13pt}
		\left\{
		\matrix
		\\
		\noalign{\vskip16pt}
		\\
		\endmatrix
		\right. 
	\endmatrix &
	\hskip-5pt
	\matrix
		\format \l & \l & \l \\
		\matrix
			\format \l & \l \\
			\matrix
				\format \l \\
				\noalign{\vskip5pt}
				\hskip-1pt
				d\nmid d_E \biggm\{ \\
			\endmatrix &
			\hskip-1pt
			\matrix
				\format \l & \l \\
				h(K_{\text{gen}})=
				\frac{h(K)}{[K_{\text{gen}}:K]} \biggm\{ &
				\matrix
					\format \l \\
					h(K)=1 \\
					\noalign{\smallskip}
					h(K)>1
				\endmatrix \\
				h(K_{\text{gen}})>
				\frac{h(K)}{[K_{\text{gen}}:K]} &
			\endmatrix
		\endmatrix &
		\hskip-5pt
		\left.
		\matrix
			\format \l & \c \\
			\cdots & K_{\text{ur}}=K \\
			\noalign{\smallskip}
			\cdots & K_{\text{ur}}=K_1 \\
			\noalign{\smallskip}
			\cdots & K_{\text{ur}}=K_2 \\
		\endmatrix
		\right\} &
		K_{\text{ur}}=(K_{\text{gen}})_1 \\
		\noalign{\smallskip}
		\matrix
			\format \l \\
			\matrix
				\format \l & \l \\
				\hskip-1pt
				d\mid d_E \Bigm\{ &
				\matrix
					\format \l \\
					d=d_E\\
					\noalign{\smallskip}
					d=d'd_E\ 
					(d'\text{\,fundamental quadratic discriminant})
				\endmatrix
			\endmatrix \\
		\endmatrix &
		\hskip-5pt
		\left.
		\matrix
			\format \l & \c \\
			\cdots & K_{\text{ur}}=K_2 \\
			\noalign{\smallskip}
			\cdots & K_{\text{ur}}=K_3 \\
		\endmatrix
		\right\} &
		K_{\text{ur}}\supsetneqq (K_{\text{gen}})_1
	\endmatrix
\endmatrix
$$
\tenpoint
\enddocument
