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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2104.03299 |
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| _version_ | 1866913470048370688 |
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| author | Yin, Wei |
| author_facet | Yin, Wei |
| contents | The groups of units $U^i_L$ of a local field $L$ play an important role in algebraic number theory, especially in class field theoretic topics. Therefore, it is interesting to study these groups from a cohomological point of view. In this article, we study and compute the first cohomology of $U_L^1$, $U^2_L$ and $U^3_L$ under certain mild hypotheses, and discuss some results about general $U^i_L$'s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03299 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the First Cohomology of Local Units Yin, Wei Number Theory The groups of units $U^i_L$ of a local field $L$ play an important role in algebraic number theory, especially in class field theoretic topics. Therefore, it is interesting to study these groups from a cohomological point of view. In this article, we study and compute the first cohomology of $U_L^1$, $U^2_L$ and $U^3_L$ under certain mild hypotheses, and discuss some results about general $U^i_L$'s. |
| title | On the First Cohomology of Local Units |
| topic | Number Theory |
| url | https://arxiv.org/abs/2104.03299 |