Motivic infinite loop spaces

IF 1.8 2区 数学 Q1 MATHEMATICS
E. Elmanto, Marc Hoyois, Adeel A. Khan, V. Sosnilo, Maria Yakerson
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引用次数: 43

Abstract

We prove a recognition principle for motivic infinite P1-loop spaces over an infinite perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of E-infinity-spaces. A framed motivic space is a motivic space equipped with transfers along finite syntomic morphisms with trivialized cotangent complex in K-theory. Our main result is that grouplike framed motivic spaces are equivalent to the full subcategory of motivic spectra generated under colimits by suspension spectra. As a consequence, we deduce some representability results for suspension spectra of smooth varieties, and in particular for the motivic sphere spectrum, in terms of Hilbert schemes of points in affine spaces.
Motivic无限循环空间
证明了无限完美域上动机无限p1环空间的一个识别原理。这是通过发展框架动力空间理论来实现的,这是e -无限空间理论的动力模拟。框架动机空间是指在k理论中具有沿有限同切复合体迁移的动机空间。我们的主要结果是:类群框架动力空间等价于悬架谱在极限下生成的动力谱的完整子范畴。因此,我们用仿射空间中点的希尔伯特格式,推导出光滑变体的悬架谱,特别是动力球谱的可表示性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.10
自引率
0.00%
发文量
7
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