Characteristic class and the $\varepsilon $-factor of an étale sheaf
Characteristic class and the $\varepsilon $-factor of an étale sheaf
复制标题
étale 捆的特征类别和 $varepsilon $ 因子
DOI：
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发表时间：
2017
影响因子：
1.3
通讯作者：
Yigeng Zhao
中科院分区：
文献类型：
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作者：
Naoya Umezaki;Enlin Yang;Yigeng Zhao
利用层的特征类证明了有限域上投射光滑簇上可构造层的一个扭曲因子公式。该公式是Kato和Saito在[Ann. Math.，168（2008）：33-96，Conjecture 4.3.11].我们给出了扭公式的两个应用。首先，我们证明了有限域上投射光滑簇上的可构造Etale层的特征类与适当的推进相容。其次，我们证明了文献中的两个Swan类在有限域上的真光滑曲面上是相同的。
We prove a twist formula for the epsilon factor of a constructible sheaf on a projective smooth variety over a finite field in terms of characteristic class of the sheaf. This formula is a modified version of the formula conjectured by Kato and Saito in [Ann. Math., 168 (2008):33-96, Conjecture 4.3.11]. We give two applications of the twist formula. Firstly, we prove that the characteristic classes of constructible \'etale sheaves on projective smooth varieties over a finite field are compatible with proper push-forward. Secondly, we show that the two Swan classes in the literature are the same on proper smooth surfaces over a finite field.