Séminaire de géométrie du 18 novembre 2026 à 14h - salle de conférences du CMLS

Abstract: The classical Riemann–Roch theorem for algebraic curves relates the geometry of divisors to the cohomology of line bundles. A tropical analogue of this theorem was established by Baker and Norine for finite graphs and subsequently extended to metric graphs. However, unlike its algebraic counterpart, tropical Riemann–Roch has traditionally been proved using combinatorial methods rather than via cohomology.

In this talk, I will introduce K-tropical curves, which are metric graphs equipped with a sheaf of rings arising from K-affine structures. These algebraic structures allow us to develop analogues of line bundles and their cohomology in the tropical setting. I will explain how this framework leads to a version of Serre duality and a cohomological approach to the tropical Riemann–Roch theorem. This is joint work with Joe Rabinoff.