The Beilinson--Bloch heights of generalized Ceresa cycles

Abstract

We compute the Beilinson--Bloch height of the generalized Ceresa cycle $\mathrm{Ce}(V)=\frac{1}{2}(V-[-1{]}_{\ast }V)$ for any cycle $V$ of pure dimension $d$ on an abelian variety $A$, in terms of an arithmetic intersection number of a certain adelic line bundle. As an application, we prove that this height is given by an adelic line bundle over algebraic families.

arXiv comment14 pages. Add a section on the relevant notations and disclose the use of AI. Comments welcome!