THE CERESA CLASS: TROPICAL, TOPOLOGICAL AND ALGEBRAIC
THE CERESA CLASS: TROPICAL, TOPOLOGICAL AND ALGEBRAIC
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CERESA 课程：热带、拓扑和代数
DOI：
10.1017/s1474748023000506
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发表时间：
2020
影响因子：
0.9
通讯作者：
Wanlin Li
中科院分区：
文献类型：
--
作者：
Dan Corey;J. Ellenberg;Wanlin Li
Ceresa圈是附着在具有标记点的光滑代数曲线上的代数循环，当曲线是具有标记点的超椭圆曲线时，该点是平凡的。Ceresa循环在某个循环类映射下的映象提供了一个称为Ceresa类的类内上同调。对于非超椭圆曲线，显式描述Ceresa类通常并不容易。我们给出了这个问题的一个“组合化”，解释了如何定义热带代数曲线的Ceresa类，以及赋有多个交换Dehn扭集的拓扑曲面(其中它与映射类群上的Morita上循环有关)。我们解释了它们与上光滑代数曲线的Ceresa类之间的关系
$\mathbb{C}(\！(T)\！)$
并证明了在这些设置中的Ceresa级是挠率。
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 nonhyperelliptic 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.