Nisnevich descent for K -theory of Deligne-Mumford stacks

Abstract

We show localization, excision and descent theorems for K -theory of Deligne-Mumford stacks. Our approach employs the Nisnevich site which is a complete, regular and bounded cd -structure on the category of such stacks and restricts to the usual Nisnevich site on schemes. By combining excision with a refinement of localization sequences due to Krishna and Toen, we show that K -theory of perfect complexes on tame Deligne-Mumford stacks satisfies Nisnevich descent.