On units with Galois complex conjugates of equal absolute value
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915020872351744 |
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| author | Deaconu, Stefan |
| author_facet | Deaconu, Stefan |
| contents | We prove, using a theorem of Northcott, that if a number field K with s real embeddings and 2t complex ones has a group of units U such that all elements in U have all its complex conjugates of same absolute value, then one necessarily has t = 1. This fact has an interesting implication in complex hermitian geometry, namely it describes all Oeljeklaus-Toma manifolds carrying locally conformally Kahler structures. It is then shown that the same method also works for the situation concerning the existence of pluriclosed metrics on Oeljeklaus-Toma manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_18958 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On units with Galois complex conjugates of equal absolute value Deaconu, Stefan Number Theory We prove, using a theorem of Northcott, that if a number field K with s real embeddings and 2t complex ones has a group of units U such that all elements in U have all its complex conjugates of same absolute value, then one necessarily has t = 1. This fact has an interesting implication in complex hermitian geometry, namely it describes all Oeljeklaus-Toma manifolds carrying locally conformally Kahler structures. It is then shown that the same method also works for the situation concerning the existence of pluriclosed metrics on Oeljeklaus-Toma manifolds. |
| title | On units with Galois complex conjugates of equal absolute value |
| topic | Number Theory |
| url | https://arxiv.org/abs/2310.18958 |