Bounding the Iwasawa invariants of Selmer groups
Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1390-1422
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We study the growth of p-primary Selmer groups of abelian varieties with good ordinary reduction at p in ${{Z}}_p$-extensions of a fixed number field K. Proving that in many situations the knowledge of the Selmer groups in a sufficiently large number of finite layers of a ${{Z}}_p$-extension over K suffices for bounding the over-all growth, we relate the Iwasawa invariants of Selmer groups in different ${{Z}}_p$-extensions of K. As applications, we bound the growth of Mordell–Weil ranks and the growth of Tate-Shafarevich groups. Finally, we derive an analogous result on the growth of fine Selmer groups.
Mots-clés :
Fukuda module, Selmer group, Mordell–Weil rank, fine Selmer group
Kleine, Sören. Bounding the Iwasawa invariants of Selmer groups. Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1390-1422. doi: 10.4153/S0008414X20000553
@article{10_4153_S0008414X20000553,
author = {Kleine, S\"oren},
title = {Bounding the {Iwasawa} invariants of {Selmer} groups},
journal = {Canadian journal of mathematics},
pages = {1390--1422},
year = {2021},
volume = {73},
number = {5},
doi = {10.4153/S0008414X20000553},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000553/}
}
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