# Algebra/Number Theory Seminar

## A more geometric approach to specialization of canonical heights

Alexander Carney, URochester

Thursday, September 23rd, 2021
2:00 PM - 3:00 PM
Hylan 1106A and Zoom

Canonical heights, for example the N\’eron-Tate height on an abelian variety, are one of the key tools for studying both abelian varieties and algebraic dynamical systems. Given a family $$X\to T$$ of dynamical systems with a section $$P:T\to X$$, the content of several theorems and conjectures is essentially that the canonical height of $$P_t$$ on each fiber should be given by a height $$h_P$$ on $$T$$. I’ll show how, using adelic line bundles, this problem can be translated into arithmetic intersection theory, and prove the corresponding statement for a one-parameter family of abelian varieties.