Tipo Seminário: Seminário de Pós-Graduação, Seminário COPGA
Palestrante(s): Oliver Lorscheid, Instituto de Matemática Pura e Aplicada
Horário/Local: 14:00-15:30(Auditorio B)
The tropicalization of a classical variety can be seen as a combinatorial gadget that allows us to study certain properties of the classical variety. This technique has been successfully applied to various problems in algebraic geometry.
Recently, Jeffrey and Noah Giansiracusa have endowed tropicalizations with the structure of a semiring scheme, a notion that emerged from F1-geometry. It is expected that this aproach will provide a more sophisticated foundation for tropical geometry and that it will allow for a deeper understanding of various combinatorial techniques in the area.
In this talk, we will first review the concepts of a tropical variety and of tropicalizations, and then motivate what a tropical scheme should be and why we are interested in such objects.