Motivic 与 Étale Spanier-Whitehead 对偶及 Becker-Gottlieb 转移
Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
AI总结：
本文基于Spanier-Whitehead对偶发展Becker-Gottlieb转移理论，适用于光滑拟射影簇的motivic与étale设置，并应用于torsor及Borel型等变motivic上同调，获得广义motivic上同调中的稳定分裂。
摘要：
本文发展了一种基于 Spanier-Whitehead 对偶的 Becker-Gottlieb 转移理论，该理论在尽可能广泛的背景下同时适用于光滑拟射影簇的 motivic 与 étale 设置：例如，适用于所有特征下非可分闭域上的簇，同时也适用于 étale 与 motivic 两种设置。鉴于传统 Becker-Gottlieb 转移最有前景的应用在于 torsor 和 Borel 型等变上同调理论，我们将应用聚焦于 torsor 的 motivic 上同调理论以及 Borel 型等变 motivic 上同调理论，两者均相对于 motivic 谱定义。我们在此方向上获得了若干结果，包括广义 motivic 上同调理论中的稳定分裂。更多进一步的应用将在后续论文中讨论。
英文摘要：
In this paper, we develop a theory of Becker-Gottlieb transfer based on Spanier-Whitehead duality that holds in both the motivic and étale settings for smooth quasi-projective varieties in as broad a context as possible: for example, for varieties over non-separably closed fields in all characteristics, and also for both the étale and motivic settings. In view of the fact that the most promising applications of the traditional Becker-Gottlieb transfer has been to torsors and Borel-style equivariant cohomology theories, we focus our applications to motivic cohomology theories for torsors as well as Borel-style equivariant motivic cohomology theories, both defined with respect to motivic spectra. We obtain several results in this direction, including a stable splitting in generalized motivic cohomology theories. Various further applications will be discussed in forthcoming papers.
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