Growth of p-parts of ideal class groups and fine Selmer groups in ℤ_q-extensions with p≠ q

2023/02/27 by Kundu, Debanjana, Lei, Antonio
#11J95 #11R20 #11R23 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.13744

Abstract

Fix two distinct odd primes p and q. We study "p≠ q" Iwasawa theory in two different settings. 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 ℤ_q-extension of K. Let F be a number field and let A_/F be an abelian variety with A[p]⊆ A(F). We give sufficient conditions for the p-part of the fine Selmer groups of A over finite subextensions of a ℤ_q-extension of F to stabilize.

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