Stabilization for Iwasawa modules in -extensions
Andrea Bandini
Università degli Studi di Parma, ItalyFabio Caldarola
Università degli Studi della Calabria, Arcavacata di Rende (Cosenza), Italy
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Abstract
Let be a -extension of a number field with layers . Let be the map induced by inclusion between the -parts of the class groups of and (). We study the capitulation kernels and to give some explicit formulas for their size and prove stabilization properties for their orders and -ranks. We also briefly investigate stabilization properties for the cokernel of and for the kernels of the norm maps and point out their relations with the nullity of the Iwasawa invariants for .
Cite this article
Andrea Bandini, Fabio Caldarola, Stabilization for Iwasawa modules in -extensions. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 137–155
DOI 10.4171/RSMUP/136-10