HomeAboutPeopleEventsResearchRTGGuest ProgrammeImpressum

There is an action of K-theory on G-theory, as observed by Quillen and later Thomason–Trobaugh. In recent work, Fangzhou Jin internalized this story to SH by constructing a representing object GGL for G-theory in the six functor formalism of KGL-modules in the motivic homotopy category. The object GGL is stable under exceptional pullback and coincides with KGL over any regular base. It is thus reasonable to ask whether GGL is a dualizing object for KGL-modules. For an excellent base in characteristic zero this follows from general duality results by Bondarko–Déglise. We give a slight generalization of this to excellent schemes of characteristic zero with different techniques. In positive characteristic the result goes through for a base which is finitely presented over a perfect field, after inverting the prime characteristic (again by Bondarko–Déglise). We give an intrinsic construction of SH[1/p] in terms of perfection understood as inverting universal homeomorphisms. We expect this will allow for a future duality result in certain mixed characteristic cases.

Based on joint work with Christian Dahlhausen and Storm Wolters. The question of GGL as dualizing object was posed to us by Denis-Charles Cisinski.