Iwasawa模的环原子猜想和半简单性

IF 0.5 3区数学 Q3 MATHEMATICS

Acta Arithmetica Pub Date : 2022-11-17 DOI:10.4064/aa221123-27-4

J. Jaulent

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引用次数: 0

摘要

我们证明了在前一篇文章中引入的关于T-分支S-分裂Iwasawa模的特征多项式并由阿贝尔域满足的分圆猜想控制了所有有限不相交集S和T的不动点子模的Z${\ell}$-秩。最后，在CM的情况下，我们证明了分圆猜想的弱版本和强版本都等价于Leopoldt和Gross-Kuz'min的经典猜想的结合。

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Conjecture cyclotomique et semi-simplicité des modules d’Iwasawa

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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