Metadata
Abstract
Let be a reductive group over a number field or -adic field, and let be a faithful representation of . A lattice in induces an integral model of . The first main result of this paper states that up to the action of the normalizer of , there are only finitely many yielding the same . We first prove this for split via the theory of Lie algebra representations, then for nonsplit via Bruhat–Tits theory. The second main result shows that in a moduli space of principally polarized abelian varieties, a special subvariety is determined, up to finite ambiguity, by its integral Mumford–Tate group. We obtain this result by applying the first main result to the symplectic representations underlying special subvarieties.
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