For abelian varieties over global fields with multiplication by an order, the Selmer group is the intersection of two maximal isotropic subspaces in an orthogonal, symplectic, unitary, or split unitary quadratic space.
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Quadratic spaces and Selmer groups of abelian varieties with multiplication
For abelian varieties over global fields with multiplication by an order, the Selmer group is the intersection of two maximal isotropic subspaces in an orthogonal, symplectic, unitary, or split unitary quadratic space.