Does there exists a reductive group $G$ of type $E_7$ over a given totally real field $L^+$ such that for every embedding $\tau:L^+\to \mathbb{R}$ except one , $G_{\tau,\mathbb{R}}(\mathbb{R})$ is compact? Is there a way to construct a group with a given number of compact form?
An algebraic group $G$ over $L^+$ such that $G_{\mathbb{R}}$ is compact for almost all embedings
ALi1373
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