Speaker: Oliver Lorscheid
Title: Scheme theoretic tropicalization
Abstract:
Recent work of Jeff and Noah Giansiracusa exhibits a scheme theoretic
structure for tropicalizations of classical varieties in terms of
so-called semiring schemes. This works well in the framework of
closed subvarieties of toric varieties, and Maclagan and Rincon
recover the structure of a polyhedral complex from the scheme
theoretic tropicalization of a variety embedded into a torus.
In this talk, I will review these ideas and show how these results can
be extended by using blue schemes. This leads to an intrinsic notion
of a tropicalization, independent from an embedding into an ambient
space, and generalizes the above mentioned results to the broader
context of log-schemes.