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W3088950324 abstract "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 'etale 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." @default.
W3088950324 created "2020-10-01" @default.
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W3088950324 date "2020-09-22" @default.
W3088950324 modified "2023-09-23" @default.
W3088950324 title "The Ceresa class: tropical, topological, and algebraic" @default.
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W3088950324 doi "https://doi.org/10.48550/arxiv.2009.10824" @default.
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