Time：15:00-16:00, Thursday, November 13 2025
Venue：E4-233
Speaker：Michal Szachniewicz, Harvard University
Title：One variable extensions of Globally Valued Fields
Abstract：I will report on a work in progress with Weronika Czerniawska. Globally Valued Fields are a generalization of global fields and within this framework one can ask how can the global structure on algebraic numbers (or more general globally valued field) be extended when one transcendental variable is added. The choice of extension corresponds to a choice of a measure on the Berkovich analytification of the projective line over algebraic integers (and can be conveniently described using the language of adelic curves in general). I will define properties of a GVF called multiplicative and additive fullness, that are first order (in the sense of unbounded continuous logic) and satisfied in existentially closed GVFs. Next I will outline a strategy to get a partial converse, namely that multiplicative and additive fullness imply existential closedness for one variable extensions of GVFs. The function field version of this result is due to Ben Yaacov.
