The Ceresa class: tropical, topological, and algebraic

Abstract: The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve, which is trivial in the Chow ring when the curve is hyperelliptic. Its image under a cycle class map provides a class in étale cohomology called the Ceresa class. There are few examples where the Ceresa class is known for non-hyperelliptic curves. We explain how to define a Ceresa class for a tropical algebraic curve, and also for a Riemann surface endowed with a multiset of commuting Dehn twists (where it is related to the Morita cocycle on the mapping class group). Finally, we explain how these are related to the Ceresa class of a smooth algebraic curve over C((t)), and show that in this setting the Ceresa class is torsion.​

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar