Aitor Iribar Lopez: Multiplication by n map on tropical and degenerate abelian varieties

Title: Multiplication by n map on tropical and degenerate abelian varieties

Abstract: Beauville was the first to use the action of the multiplication by n maps on the Chow ring of an abelian variety to derive interesting cycle theoretic consequences. In recent work with Bae, Feusi and Molcho, we study how this action behaves when the abelian variety is allowed to degenerate "to torus rank at most 1". This leads us to study the action of multiplication by N and Brion's formula on the tropical abelian varieties that control the degeneration. In the talk, I will try to explain how we use these combinatorial calculations to deduce almost the same results as one gets on an abelian scheme: a multiplicative filtration by weights, a Fourier transform, and a formula for the zero section