Ceresa cycles of modular curves

Abstract: The Ceresa cycle is an algebraic cycle attached to smooth algebraic curve with a marked point, which is always homologically trivial. Ceresa proved that for a very general complex curve of genus at least 3, this cycle is not trivial as an element of the Chow group. Notably, hyperelliptic curves with a Weierstrass point have trivial Ceresa cycle. There are few other explicit examples where triviality/non-triviality is known. In this talk I will discuss the non-vanishing of the Ceresa cycle attached to the modular curve $X_0(N)$.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html