On the rank of Leopoldt's and Gross's regulator maps
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866918325266677760 |
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| author | Maksoud, Alexandre |
| author_facet | Maksoud, Alexandre |
| contents | We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of Gross's finiteness conjecture (also known as the Gross-Kuz'min conjecture) beyond the classical abelian case, and we show that Gross's $p$-adic regulator has at least half of the conjectured rank. We also describe and compute non-cyclotomic analogues of Gross's defect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08203 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the rank of Leopoldt's and Gross's regulator maps Maksoud, Alexandre Number Theory We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of Gross's finiteness conjecture (also known as the Gross-Kuz'min conjecture) beyond the classical abelian case, and we show that Gross's $p$-adic regulator has at least half of the conjectured rank. We also describe and compute non-cyclotomic analogues of Gross's defect. |
| title | On the rank of Leopoldt's and Gross's regulator maps |
| topic | Number Theory |
| url | https://arxiv.org/abs/2201.08203 |