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arXiv · 2405.19601

On the Serre conjecture for Artin characters in the geometric case

Tomoyuki Abe
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Abstract

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.

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Tomoyuki Abe. 2024-05-30. On the Serre conjecture for Artin characters in the geometric case. https://arxiv.org/abs/2405.19601

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