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Nisnevich descent for K-theory of Deligne-Mumford stacks

Published online by Cambridge University Press:  18 October 2011

Amalendu Krishna  and
Paul Arne Østvær
Amalendu Krishna
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai,India, amal@math.tifr.res.in
Paul Arne Østvær
Affiliation:
Department of Mathematics, University of Oslo, Norway, paularne@math.uio.no
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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 Töen, we show that K-theory of perfect complexes on tame Deligne-Mumford stacks satisfies Nisnevich descent.

Keywords

Deligne-Mumford stacksK-theory of perfect complexesNisnevich descent
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 2 , April 2012 , pp. 291 - 331
Copyright
Copyright © ISOPP 2011

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