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arXiv · 2211.09586

Cyclotomic conjecture and semi-simplicity of S-split T-ramified Iwasawa modules

Jean-François Jaulent
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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 Z${\ell}$-rank of the submodule of fixed points for all finite disjoint sets S and T of places.Last, in the CM-case we prove that the weak and the strong versions of the cyclotomic conjecture both are equivalent to the conjunction of the classical conjectures of Leopoldt and Gross-Kuz'min.

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Jean-François Jaulent. 2022-11-17. Cyclotomic conjecture and semi-simplicity of S-split T-ramified Iwasawa modules. https://arxiv.org/abs/2211.09586

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