On a new invariant determining the isomorphism classes of \(\Lambda \)-modules with \(\lambda =3\)

Abstract

For a prime number p and the ring of power series \(\Lambda ={\mathbb {Z}}_p[[T]]\), we define a new invariant which determines the isomorphism classes of finitely generated torsion \(\Lambda \)-modules with \(\lambda =3\). We apply this result to the classical Selmer group attached to an elliptic curve over \({\mathbb {Q}}\).

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Acknowledgements

.The author would like to thank Professor Masato Kurihara for his valuable suggestions, which led me to get the results in this paper. The author also would like to express his gratitude to the referee for reading this article carefully and giving many helpful suggestions. The author is partially supported by JSPS Core-to-core program, Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory.

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Correspondence to Kazuaki Murakami.

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Murakami, K. On a new invariant determining the isomorphism classes of \(\Lambda \)-modules with \(\lambda =3\). manuscripta math. 164, 409–430 (2021). https://doi.org/10.1007/s00229-020-01190-6

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Mathematics Subject Classification

  • Primary 11R23
  • Secondary 11G05