Heights, abelian varieties, and tropical geometry

Abstract: I will describe some connections between arithmetic geometry of abelian varieties, non-archimedean/tropical geometry, and combinatorics. For a principally polarized abelian variety, we show an identity relating the Faltings height and the Néron--Tate height (of a symmetric effective divisor defining the polarization) which involves invariants arising from non-archimedean/tropical geometry. If time permits, we also give formulas for (non-archimedean) canonical local heights in terms of tropical invariants. (Based on joint work with Robin de Jong)

algebraic geometry

Audience: researchers in the topic

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com