Growth of -parts of ideal class groups and fine Selmer groups in \mathbb Z_q-extensions with p\ne q
Tom 207 / 2023
Acta Arithmetica 207 (2023), 297-313
MSC: Primary 11R23; Secondary 11R29, 11R20, 11J95.
DOI: 10.4064/aa220518-28-2
Opublikowany online: 11 April 2023
Streszczenie
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.
