论文标题
小组理论约翰逊课程和带有扭转室类的非混血儿曲线
Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class
论文作者
论文摘要
令L为素数，并具有无扭转的Abelianization的支持。我们生成了J Johnson/Morita Cocycle的群体理论类似物 - 对于表面组，当L = 2时，这些同伴似乎可以完善现有的构造。我们将其应用于平滑曲线的Pro-L Etale基本组，以获得Galois-Cohomology类似物，并讨论了它们与Hain和Matsumoto的工作的关系。我们分析了这些类别的许多基本属性，并使用它们来举例说明非混血曲线的Ceresa类在L-Adic Abel-Jacobi地图下具有扭转图像。
Let l be a prime and G a pro-l group with torsion-free abelianization. We produce group-theoretic analogues of the Johnson/Morita cocycle for G -- in the case of surface groups, these cocycles appear to refine existing constructions when l=2. We apply this to the pro-l etale fundamental groups of smooth curves to obtain Galois-cohomological analogues, and discuss their relationship to work of Hain and Matsumoto in the case the curve is proper. We analyze many of the fundamental properties of these classes and use them to give an example of a non-hyperelliptic curve whose Ceresa class has torsion image under the l-adic Abel-Jacobi map.
