Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2408.15975 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929478056280064 |
|---|---|
| author | Hirose, Minoru |
| author_facet | Hirose, Minoru |
| contents | Let $N$ be a power of $2$ or $3$, and $μ_{N}$ the set of $N$-th roots of unity. We show that the ring of motivic periods of Mixed Tate motives over $\mathbb{Z}[μ_{N},\frac{1}{N}]$ is spanned by the motivic cyclotomic multiple zeta values of level $N$. This implies that the action of the motivic Galois group of mixed Tate motives over $\mathbb{Z}[μ_{N},\frac{1}{N}]$ on the motivic fundamental group of $\mathbb{G}_{m}-μ_{N}$ is faithful. This is a generalization of the known results for $N\in\{1,2,3,4,8\}$ by Deligne and Brown. We also discuss cyclotomic multiple zeta values of weight $2$ of other levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixed Tate motives and cyclotomic multiple zeta values of level $2^n$ or $3^n$ Hirose, Minoru Number Theory 11G55, 11M32, 14C15, 14F42 Let $N$ be a power of $2$ or $3$, and $μ_{N}$ the set of $N$-th roots of unity. We show that the ring of motivic periods of Mixed Tate motives over $\mathbb{Z}[μ_{N},\frac{1}{N}]$ is spanned by the motivic cyclotomic multiple zeta values of level $N$. This implies that the action of the motivic Galois group of mixed Tate motives over $\mathbb{Z}[μ_{N},\frac{1}{N}]$ on the motivic fundamental group of $\mathbb{G}_{m}-μ_{N}$ is faithful. This is a generalization of the known results for $N\in\{1,2,3,4,8\}$ by Deligne and Brown. We also discuss cyclotomic multiple zeta values of weight $2$ of other levels. |
| title | Mixed Tate motives and cyclotomic multiple zeta values of level $2^n$ or $3^n$ |
| topic | Number Theory 11G55, 11M32, 14C15, 14F42 |
| url | https://arxiv.org/abs/2408.15975 |