Cofinality of formal Gubler models

Algebra Seminar
Friday, November 16, 2018 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Tyler Foster – Florida State University –
Yoav Len
Let K be a non-trivially valued non-Archimedean field, R its valuation subring. A formal Gubler model is a formal R-scheme that comes from a polyhedral decomposition of a tropical variety. In this talk, I will present joint work with Sam Payne in which we show that any formal model of any compact analytic domain V inside a (not necessarily projective) K-variety X can be dominated by a formal Gubler model that extends to a model of X. This result plays a central role in our work on "structure sheaves" on tropicalizations and our work on adic tropicalization. If time permits I will explain some of this work.