On Krull-Schmidt decompositions of unit groups of number fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911797960769536 |
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| author | Kumon, Asuka Lim, Donghyeok |
| author_facet | Kumon, Asuka Lim, Donghyeok |
| contents | 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 $p^{3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Krull-Schmidt decompositions of unit groups of number fields Kumon, Asuka Lim, Donghyeok Number Theory 11R27, 11R33, 20C10 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 $p^{3}$. |
| title | On Krull-Schmidt decompositions of unit groups of number fields |
| topic | Number Theory 11R27, 11R33, 20C10 |
| url | https://arxiv.org/abs/2403.09420 |