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k-theory of perfect complexes

Journal of K-Theory (1)

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Nisnevich descent for K-theory of Deligne-Mumford stacks
Amalendu Krishna, Paul Arne Østvær
Journal:

Journal of K-Theory / Volume 9 / Issue 2 / April 2012

Published online by Cambridge University Press:

18 October 2011, pp. 291-331

Print publication:

April 2012
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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 Töen, we show that K-theory of perfect complexes on tame Deligne-Mumford stacks satisfies Nisnevich descent.