Article
| Title: | A twisted class number formula and Gross's special units over an imaginary quadratic field (English) |
| Author: | El Boukhari, Saad |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1333-1347 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $F/k$ be a finite abelian extension of number fields with $k$ imaginary quadratic. Let $O_F$ be the ring of integers of $F$ and $n\geq 2$ a rational integer. We construct a submodule in the higher odd-degree algebraic $K$-groups of $O_F$ using corresponding Gross's special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher ``twisted'' class number of $F$, which is the cardinal of the finite algebraic $K$-group $K_{2n-2}(O_F)$. (English) |
| Keyword: | algebraic $K$-theory |
| Keyword: | Dedekind zeta function |
| Keyword: | Artin $L$-function |
| Keyword: | Beilinson regulator |
| Keyword: | generalized index |
| Keyword: | Lichtenbaum conjecture |
| MSC: | 11R70 |
| MSC: | 19F27 |
| idZBL: | Zbl 07790577 |
| DOI: | 10.21136/CMJ.2023.0067-23 |
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| Date available: | 2023-11-23T12:30:28Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151963 |
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