Nontrivial Ceresa and modified diagonal classes via semistable reduction

Abstract: The Ceresa class is a canonical, cohomologically trivial algebraic cycle on the Jacobian of a curve. Modified diagonal classes are closely related, and almost equivalent, algebraic cycles defined on the triple product of the curve with itself. These canonical cycles are known to be non-torsion in the Chow group for sufficiently general curves, but the proof is not explicit. It is therefore interesting to ask for which curves these cycles are non-torsion.

This talk is about joint work with Ari Shnidman, in which we calculate the ramification of an l-adic Abel-Jacobi image of a modified diagonal class for any semistable curve over a finite extension of Z_p. The calculation is in terms of purely combinatorial data on the special fiber. As an application, we are able to give new and explicit conditions under which a curve over a number field has nonzero or nontorsion Ceresa class.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar