Let $G$ be a finite group acting freely on a smooth projective scheme $X$ over a locally compact field of characteristic 0. We show that the $varepsilon_0$-constants associated to symplectic representations $V$ of $G$ and the action of $G$ on $X$ may be determined from Pfaffian invariants associated to duality pairings on Hodge cohomology. We also use such Pfaffian invariants, along with equivariant Arakelov Euler characteristics, to determine hermitian Euler characteristics associated to tame actions of finite groups on regular projective schemes over $mathbb{Z}$.
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机译：假设$ G $是在特征为0的局部紧凑域上，在光滑投影方案$ X $上自由起作用的有限群。我们证明，与$ G $的辛表示$ V $相关联的$ varepsilon_0 $-常数和作用可以从与Hodge同源性的对偶配对相关的Pfaffian不变量确定$ G $在$ X $上的$ G $。我们还使用此类Pfaffian不变量以及等变量Arakelov Euler特征来确定与在$ mathbb {Z} $上的常规投影方案上有限群的驯服动作相关的Hermitian Euler特征。
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