Shubhodip Mondal (Purdue): Formal deformations of syntomic cohomology

Abstract: I will explain how the notion of de Rham Witt complexes becomes "representable" in a certain sense in the category of F-gauges. This should be viewed as an algebraic analogue of the representability of TR in the world of cyclotomic spectra as proven in the work of Blumberg-Mandell and McCandless. I will explain certain consequences of this result in studying deformations of syntomic cohomology and recover a result previously proven in my joint work with Devalapurkar. A key technical role is played by the notion of [p]-graded F-gauges, which will be introduced in the talk. This is joint work with Elden Elmanto.