On the Serre conjecture for Artin characters in the geometric case
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913890538881024 |
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| author | Abe, Tomoyuki |
| author_facet | Abe, Tomoyuki |
| contents | Let $G$ be a finite group and $A$ be a regular local ring on which $G$ acts. Under certain assumptions on $A$ and the action, Serre defined a function $a_G\colon G\rightarrow\mathbb{Z}$ which can be viewed as a higher dimensional analogue of Artin character, and conjectured that it is associated to a $\mathbb{Q}_\ell$-rational representation of $G$ for any prime $\ell$ invertible in $A$. We prove this conjecture in the equal characteristic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Serre conjecture for Artin characters in the geometric case Abe, Tomoyuki Number Theory Algebraic Geometry Let $G$ be a finite group and $A$ be a regular local ring on which $G$ acts. Under certain assumptions on $A$ and the action, Serre defined a function $a_G\colon G\rightarrow\mathbb{Z}$ which can be viewed as a higher dimensional analogue of Artin character, and conjectured that it is associated to a $\mathbb{Q}_\ell$-rational representation of $G$ for any prime $\ell$ invertible in $A$. We prove this conjecture in the equal characteristic case. |
| title | On the Serre conjecture for Artin characters in the geometric case |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2405.19601 |