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.

Add to your calendar

Download event information as iCalendar file (only this event)