Stabilization for Iwasawa modules in p -extensions
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 137-155.

Let K/k be a 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 (mn). We study the capitulation kernels H n,m := ker (i n,m ) and H n := mn 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.

DOI : 10.4171/RSMUP/136-10
Classification : 11
Mots-clés : $\mathbb Z_p-extensions, Iwasawa modules, Iwasawa invariants
Bandini, Andrea 1 ; Caldarola, Fabio 2

1 Università degli Studi di Parma, PARMA, ITALY
2 Università degli Studi della Calabria, ARCAVACATA DI RENDE (COSENZA), ITALY
@article{RSMUP_2016__136__137_0,
     author = {Bandini, Andrea and Caldarola, Fabio},
     title = {Stabilization for {Iwasawa} modules in $\mathbb Z_p$-extensions},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {137--155},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
     doi = {10.4171/RSMUP/136-10},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-10/}
}
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Bandini, Andrea; Caldarola, Fabio. Stabilization for Iwasawa modules in $\mathbb Z_p$-extensions. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 137-155. doi : 10.4171/RSMUP/136-10. http://www.numdam.org/articles/10.4171/RSMUP/136-10/

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