Differential Operators, Gauges, and Mazur’s Theorem for Hodge Modules

(Attention, horaire décalé et exposé sur Zoom.) In this talk I will explain how Mazur’s theorem about Frobenius and the Hodge filtration (from the early 1970’s) can be put into the context of filtered D-module theory. Along the way, I’ll explain the notion of a gauge, discuss Berthelot’s arithmetic differential operators, and explain how the Hodge filtration on a mixed Hodge module of geometric origin fits into the picture. I’ll give at least the basic background on all of the objects that appear in the title of the talk.