论文标题
CERESA类：热带，拓扑和代数
The Ceresa class: tropical, topological, and algebraic
论文作者
论文摘要
CERESA循环是一个代数循环，该代数循环附着在平滑的代数曲线上，具有明显的点，当曲线是高纤维化的带有明显的Weierstrass点时，这是微不足道的。在特定周期类图下CERESA循环的图像提供了称为Ceresa类的典型的同类阶级。通常，针对非高温曲线明确描述Ceresa类并不容易。我们提出了此问题的“组合化”，解释了如何为热带代数曲线定义CERESA类，以及用于与多个通勤Dehn Twists的拓扑表面（与该曲线相关的多种通勤曲线）。我们解释这些与$ \ mathbb {c}（\！（t）\！）$的平滑代数曲线的CERESA类别有关，并证明这些设置中的每一个中的Ceresa类都是扭转。
The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve with a marked point, which is trivial when the curve is hyperelliptic with a marked Weierstrass point. The image of the Ceresa cycle under a certain cycle class map provides a class in étale cohomology called the Ceresa class. Describing the Ceresa class explicitly for non-hyperelliptic curves is in general not easy. We present a "combinatorialization" of this problem, explaining how to define a Ceresa class for a tropical algebraic curve, and also for a topological surface endowed with a multiset of commuting Dehn twists (where it is related to the Morita cocycle on the mapping class group). We explain how these are related to the Ceresa class of a smooth algebraic curve over $\mathbb{C}(\!(t)\!)$, and show that the Ceresa class in each of these settings is torsion.
