## Structure of the Mordell-Weil group over the $\mathbb {Z}_p$-extensions

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## Abstract:

We study the $\Lambda$-module structure of the Mordell-Weil, Selmer, and Tate-Shafarevich groups of an abelian variety over $\mathbb {Z}_p$-extensions.## References

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## Additional Information

**Jaehoon Lee**- Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095
- Address at time of publication: Math department of KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141 South Korea
- MR Author ID: 1101046
- Email: jaehoonlee@kaist.ac.kr
- Received by editor(s): September 24, 2018
- Received by editor(s) in revised form: May 25, 2019, and June 12, 2019
- Published electronically: December 20, 2019
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**373**(2020), 2399-2425 - MSC (2010): Primary 11R23, 11Gxx
- DOI: https://doi.org/10.1090/tran/7937
- MathSciNet review: 4069223