Torsion points of a section of an abelian scheme over a p-adic field have rigid-analytic neighborhoods isolating each torsion order; a nodal-fiber example shows that bad reduction destroys this separation.
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On the $p$-adic distribution of torsion values for a section of an abelian scheme
Torsion points of a section of an abelian scheme over a p-adic field have rigid-analytic neighborhoods isolating each torsion order; a nodal-fiber example shows that bad reduction destroys this separation.