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Conjecture cyclotomique et semi-simplicité des modules d’Iwasawa

Volume 208 / 2023

Jean-François Jaulent Acta Arithmetica 208 (2023), 185-197 MSC: Primary 11R23; Secondary 11R37 DOI: 10.4064/aa221123-27-4 Published online: 15 June 2023


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.


  • Jean-François JaulentInstitut de Mathématiques de Bordeaux
    Univ. Bordeaux & CNRS
    351 Cours de la Libération
    F-33405 Talence Cedex, France

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