Two abelian varieties A1, A2 over a number field K are strongly iso-Kummerian if the torsion fields K(A1[d]) and K(A2[d]) coincide for all d >= 1. For all g >= 4 we construct geometrically simple, strongly iso-Kummerian g-dimensional abelian varieties over number fields that are not geometrically isogenous. We also discuss related examples and put significant constraints on any further iso-Kummerian pair.
Non-isogenous abelian varieties sharing the same division fields
Lombardo, D
2023-01-01
Abstract
Two abelian varieties A1, A2 over a number field K are strongly iso-Kummerian if the torsion fields K(A1[d]) and K(A2[d]) coincide for all d >= 1. For all g >= 4 we construct geometrically simple, strongly iso-Kummerian g-dimensional abelian varieties over number fields that are not geometrically isogenous. We also discuss related examples and put significant constraints on any further iso-Kummerian pair.File in questo prodotto:
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Varieties sharing the same division fields.pdf
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SameTorsionFields.pdf
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