On Krull–Schmidt decompositions of unit groups of number fields
Year: 2024
Type: article
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 $p^{3}$.
Source: Acta Arithmetica
Authors: Asuka Kumon, Donghyeok Lim
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1047533241, G3308718102, G3793286438
OpenAlex ID: W4404698917