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Growth of $p$-parts of ideal class groups and fine Selmer groups in $\mathbb Z_q$-extensions with $p\ne q$

Volume 207 / 2023

Debanjana Kundu, Antonio Lei Acta Arithmetica 207 (2023), 297-313 MSC: Primary 11R23; Secondary 11R29, 11R20, 11J95. DOI: 10.4064/aa220518-28-2 Published online: 11 April 2023


Fix two distinct odd primes $p$ and $q$. We study “$p\ne q$” Iwasawa theory in two different settings.

(1) Let $K$ be an imaginary quadratic field of class number 1 such that both $p$ and $q$ split in $K$. We show that under appropriate hypotheses, the $p$-part of the ideal class groups is bounded over finite subextensions of an anticyclotomic $\mathbb Z_q$-extension of $K$.

(2) Let $F$ be a number field and let $A_{/F}$ be an abelian variety with $A[p]\subseteq A(F)$. We give sufficient conditions for the $p$-part of the fine Selmer groups of $A$ over finite subextensions of a $\mathbb Z_q$-extension of $F$ to stabilize.


  • Debanjana KunduFields Institute
    University of Toronto
    Toronto, ON, Canada M5T 3J1
  • Antonio LeiDepartment of Mathematics and Statistics
    University of Ottawa
    Ottawa, ON, Canada K1N 6N5

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