JournalsrsmupVol. 136pp. 137–155

Stabilization for Iwasawa modules in Zp\mathbb Z_p-extensions

  • Andrea Bandini

    Università degli Studi di Parma, Italy
  • Fabio Caldarola

    Università degli Studi della Calabria, Arcavacata di Rende (Cosenza), Italy
Stabilization for Iwasawa modules in $\mathbb Z_p$-extensions cover
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Abstract

Let K/kK/k be a Zp\mathbb Z_p-extension of a number field kk with layers knk_n. Let in,mi_{n,m} be the map induced by inclusion between the pp-parts of the class groups of knk_n and kmk_m (mnm \geqslant n). We study the capitulation kernels Hn,m:=ker(in,m)H_{n,m}:=\mathrm {ker} (i_{n,m}) and Hn:=mnHn,mH_n:=\bigcup_{m \geqslant n}H_{n,m} to give some explicit formulas for their size and prove stabilization properties for their orders and pp-ranks. We also briefly investigate stabilization properties for the cokernel of im,ni_{m,n} and for the kernels of the norm maps and point out their relations with the nullity of the Iwasawa invariants for K/kK/k.

Cite this article

Andrea Bandini, Fabio Caldarola, Stabilization for Iwasawa modules in Zp\mathbb Z_p-extensions. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 137–155

DOI 10.4171/RSMUP/136-10