Bend relations, valuations, and universal tropicalization
Jeffrey Giansiracusa (University of Swansea)
Wednesday 21st October, 2015 16:00-17:00 Maths 522
Let X be a locally integral scheme over a non-archimedean valued field k. An embedding of X into a scheme equipped with a model over the field with one element F_1 determines a tropicalization of X, which is described by certain canonical equations called the 'bend relations'. The base-change adjunction between F_1 and k yields a universal embedding of X into an ambient space with F_1 model, and thus there is a universal tropicalization. Moreover, in this case solutions to the bend relations are exactly non-archimedean valuations on the structure sheaf of X. Thus the Berkovich analytification can be realized as an algebraic moduli space of valuations.