On the classification of maximal arithmetic subgroups in split groups

We obtain an explicit classification of the maximal arithmetic subgroups of the $Q$-split orthogonal groups of type $(D_l)$, where $Q$ is the field of rational numbers or the field of rational functions of one variable with finite field of constants $(\operatorname{char}Q\ne2)$. In view of known results, this completes the explicit classification of maximal arithmetic subgroups for all $Q$-split classical simple groups.
As a preliminary, we obtain an explicit solution of a local analogue of the maximality problem for split orthogonal groups of type $(D_l)$ over a non-Archimedean locally compact field of characteristic $\ne2$.
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