Fine Selmer groups and ideal class groups

Kleine, Sören; Müller, K.

doi:10.1007/s11139-022-00619-8

Ramanujan J

2022

DOI: 10.1007/s11139-022-00619-8

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Fine Selmer groups and ideal class groups

Sören Kleine

K. Müller

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2023

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Boundedness of Iwasawa Invariants of Fine Selmer Groups and Selmer Groups

Kleine¹,

Matar²

2023

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In this article we consider Selmer groups and fine Selmer groups of abelian varieties over a number field K. Following a classical approach of Monsky for Iwasawa modules from ideal class groups, we give sufficient conditions for the Iwasawa $$\mu $$ μ -invariants of the fine Selmer groups and the $$\mu $$ μ -invariants of the Selmer groups to be bounded as one runs over the $$\mathbb {Z}_p$$ Z p -extensions of K. Moreover, we describe a criterion for the boundedness of Iwasawa $$\lambda $$ λ -invariants of Selmer groups and fine Selmer groups over multiple $$\mathbb {Z}_p$$ Z p -extensions which generalises a criterion of Monsky from dimension 2 to arbitrary dimension.

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Boundedness of Iwasawa Invariants of Fine Selmer Groups and Selmer Groups

Kleine¹,

Matar²

2023

Results Math

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show abstract

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Fine Selmer groups and ideal class groups

Cited by 1 publication

References 41 publications

Boundedness of Iwasawa Invariants of Fine Selmer Groups and Selmer Groups

Boundedness of Iwasawa Invariants of Fine Selmer Groups and Selmer Groups

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