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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Non-isogenous abelian varieties sharing the same division fields
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by Davide Lombardo HTML | PDF
Trans. Amer. Math. Soc. 376 (2023), 2615-2640


Two abelian varieties $A_1, A_2$ over a number field $K$ are strongly iso-Kummerian if the torsion fields $K(A_1[d])$ and $K(A_2[d])$ coincide for all $d \geq 1$. For all $g \geq 4$ 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.
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Additional Information
  • Davide Lombardo
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
  • MR Author ID: 1143804
  • ORCID: 0000-0002-1069-3379
  • Email:
  • Received by editor(s): September 17, 2021
  • Received by editor(s) in revised form: June 23, 2022
  • Published electronically: January 18, 2023
  • Additional Notes: The author was partially supported by MIUR (Italy) through the grant PRIN 2017 “Geometric, algebraic and analytic methods in arithmetic”, and by the Università di Pisa through PRA 2018-19 “Spazi di moduli, rappresentazioni e strutture combinatorie”
  • © Copyright 2023 by the authors
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 2615-2640
  • MSC (2020): Primary 14K22, 14K15, 11F80, 11G10
  • DOI:
  • MathSciNet review: 4557876