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1 results

  • Euler characteristics and their congruences in the positive rank setting

  • Part of
  • Anwesh Ray, R. Sujatha
  • Journal:
    Canadian Mathematical Bulletin / Volume 64 / Issue 1 / March 2021
    Published online by Cambridge University Press:
    11 June 2020, pp. 228-245
    Print publication:
    March 2021

  • The notion of the truncated Euler characteristic for Iwasawa modules is an extension of the notion of the usual Euler characteristic to the case when the homology groups are not finite. This article explores congruence relations between the truncated Euler characteristics for dual Selmer groups of elliptic curves with isomorphic residual representations, over admissible p-adic Lie extensions. Our results extend earlier congruence results from the case of elliptic curves with rank zero to the case of higher rank elliptic curves. The results provide evidence for the p-adic Birch and Swinnerton-Dyer formula without assuming the main conjecture.