Conjecture cyclotomique et semi-simplicité des modules d’Iwasawa
Volume 208 / 2023
Acta Arithmetica 208 (2023), 185-197
MSC: Primary 11R23; Secondary 11R37
DOI: 10.4064/aa221123-27-4
Published online: 15 June 2023
Abstract
We show that the cyclotomic conjecture on the characteristic polynomial of $T$-ramified $S$-split Iwasawa modules, introduced in a previous paper and satisfied by abelian fields, governs the $\mathbb Z_\ell $-rank of the submodule of fixed points for all finite disjoint sets $S$ and $T$ of places.
Moreover, in the CM-case we prove that the weak and the strong versions of the cyclotomic conjecture are both equivalent to the conjunction of the classical conjectures of Leopoldt and Gross–Kuz’min.
