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arXiv · 2403.09420

On Krull-Schmidt decompositions of unit groups of number fields

Asuka Kumon·Donghyeok Lim
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Abstract

We prove that the Krull-Schmidt decomposition of the Galois module of the $p$-adic completion of algebraic units is controlled by the primes that are ramified in the Galois extension and the $S$-ideal class group. We also compute explicit upper bounds for the number of possible Galois module structures of algebraic units when the Galois group is cyclic of order $p^{2}$ or $p^{3}$.

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Asuka Kumon, Donghyeok Lim. 2024-03-14. On Krull-Schmidt decompositions of unit groups of number fields. https://arxiv.org/abs/2403.09420

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