In this talk, I will discuss some recent advances in the theory of motives in the context of rigid analytic geometry. Building on work of Ayoub, Bondarko, we provide an equivalence between the category of ‘unipotent’ rigid analytic motives over a non-archimedean field and the category of ‘monodromy maps’ M → M (−1) of algebraic motives over the residue field. This allows us to build a unified framework for the study of monodromy operators and weight filtrations of cohomology theories for varieties over a local field. As an application, we give a streamlined definition of Hyodo–Kato cohomology without recourse to log-geometry, as predicted by Fontaine, and we produce an induced Clemens–Schmid chain complex.
This is a joint work in progress with Alberto Vezzani and Martin Gallauer.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
