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

{"title":"delign - mumford堆栈K -理论的Nisnevich下降","authors":"A. Krishna, P. A. Østvær","doi":"10.1017/IS011006028JKT161","DOIUrl":null,"url":null,"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.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"291-331"},"PeriodicalIF":0.0000,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011006028JKT161","citationCount":"16","resultStr":"{\"title\":\"Nisnevich descent for K -theory of Deligne-Mumford stacks\",\"authors\":\"A. Krishna, P. A. Østvær\",\"doi\":\"10.1017/IS011006028JKT161\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"9 1\",\"pages\":\"291-331\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS011006028JKT161\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS011006028JKT161\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS011006028JKT161","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of K-Theory 数学-数学

自引率

0.00%

发文量

审稿时长

>12 weeks