Let K/k be a Z_p-extension of a number field k with layers k_n. Let i_n,m be the map induced by inclusion between the p-parts of the class groups of k_n and k_m (m>n). We study the capitulation kernels H_n,m:=ker(i_n,m) and H_n:=\cup_m>n H_n,m to give some explicit formulas for their size and prove stabilization properties for their orders and p-ranks. We also briefly investigate stabilization properties for the cokernel of i_m,n and for the kernels of the norm maps and point out their relations with the nullity of the Iwasawa invariants for K/k.

Stabilization for Iwasawa modules in Z_p-extensions

Andrea Bandini;
2016

Abstract

Let K/k be a Z_p-extension of a number field k with layers k_n. Let i_n,m be the map induced by inclusion between the p-parts of the class groups of k_n and k_m (m>n). We study the capitulation kernels H_n,m:=ker(i_n,m) and H_n:=\cup_m>n H_n,m to give some explicit formulas for their size and prove stabilization properties for their orders and p-ranks. We also briefly investigate stabilization properties for the cokernel of i_m,n and for the kernels of the norm maps and point out their relations with the nullity of the Iwasawa invariants for K/k.
Bandini, Andrea; Caldarola, Fabio
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/925092
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