delign - mumford堆栈K -理论的Nisnevich下降

Journal of K-Theory Pub Date : 2012-04-01 DOI:10.1017/IS011006028JKT161

A. Krishna, P. A. Østvær

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引用次数: 16

摘要

我们给出了Deligne-Mumford堆栈K -理论的局部化定理、切除定理和下降定理。我们的方法采用Nisnevich点，这是一个完整的、规则的、有界的cd结构，在这种堆栈的范畴上，它限制在方案上通常的Nisnevich点。通过将切除与Krishna和Toen引起的定位序列的细化相结合，我们证明了tame delign - mumford堆栈上完美复合体的K -理论满足Nisnevich下降。

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Nisnevich descent for K -theory of Deligne-Mumford stacks

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.

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Journal of K-Theory 数学-数学

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>12 weeks