动机与平展Spanier-Whitehead对偶及Becker-Gottlieb转移
代数几何
2024-04-23 v3
摘要
在本文中，我们基于Spanier-Whitehead对偶发展了一套Becker-Gottlieb转移理论，该理论在动机(motivic)与平展(\'etale)两种设定下对光滑拟射影簇在尽可能广泛的语境中成立：例如，对一切特征上非可分闭域上的簇，以及对平展与动机两种设定。鉴于传统Becker-Gottlieb转移最有前景的应用在于 torsor 与 Borel 式等变上同调理论，我们将应用聚焦于针对 torsor 的动机上同调理论以及 Borel 式等变动机上同调理论，二者均相对于动机谱定义。我们在此方向上获得若干结果，包括广义动机上同调理论中的稳定分裂。更多应用将于后续论文中讨论。
引用
@article{arxiv.2007.02247,
title = {Motivic and \'Etale Spanier-Whitehead duality and the Becker-Gottlieb transfer},
author = {Gunnar Carlsson and Roy Joshua},
journal= {arXiv preprint arXiv:2007.02247},
year = {2024}
}
备注
This is an updated version where we have made several improvements, for example, the relationship between equivariant and non-equivariant spectra that plays a rather subtle role in the construction of the transfer is discussed in detail. Showing the existence of splittings using the transfer is discussed in a short separate (new) paper that is now also available on the arXiv