摘要翻译:
本文的目的是双重的。首先,我们利用motivic Landweber精确函子定理推导出Bott倒无限射影空间是同伦代数K$-理论。这个论证比任何其他已知的证明都短得多,并很好地说明了兰德韦伯精确性的有效性。其次,我们省去了基格式的正则性假设,这是定向模环谱概念中经常隐含的要求。后者允许我们验证motivic Landweber精确函子定理和对于有限Krull维数的每一个noetherian基格式的代数协边谱的普适性。
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英文标题:
《Chern classes, K-theory and Landweber exactness over nonregular base
schemes》
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作者:
Niko Naumann, Markus Spitzweck, Paul Arne {\O}stv{\ae}r
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Algebraic Topology 代数拓扑
分类描述:Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论,同调代数,流形的代数处理
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英文摘要:
The purpose of this paper is twofold. First, we use the motivic Landweber exact functor theorem to deduce that the Bott inverted infinite projective space is homotopy algebraic $K$-theory. The argument is considerably shorther than any other known proofs and serves well as an illustration of the effectiveness of Landweber exactness. Second, we dispense with the regularity assumption on the base scheme which is often implicitly required in the notion of oriented motivic ring spectra. The latter allows us to verify the motivic Landweber exact functor theorem and the universal property of the algebraic cobordism spectrum for every noetherian base scheme of finite Krull dimension.
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PDF链接:
https://arxiv.org/pdf/0809.0267