Artin—Mazur formal groups and Milne duality via unipotent spectra

Let k be a field. We introduce new invariants for k-schemes valued in unipotent group schemes over k. To do so, we develop the notion of "unipotent spectra" — defined to be the stabilization of Toën's category of affine stacks. 

As an application, we recover the Artin—Mazur formal groups associated to schemes. Further, we show that syntomic cohomology admits a natural refinement to a perfect unipotent spectrum. Finally, we extend Milne's work on arithmetic duality theorems to perfect unipotent spectra and apply it to refine Poincaré duality in syntomic cohomology. 

This is joint work with Shubhodip Mondal and Tasos Moulinos. 

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