加性及双陪集公式：动机与艾达尔 Becker-Gottlieb 转移
Additivity and Double Coset formulae for the Motivic and Étale Becker-Gottlieb transfer
AI总结：
本文延续前期工作，证明动机及艾达尔 Becker-Gottlieb 转移的可加性，并推导双陪集公式及对可分闭域上约化群齐次空间 Brauer 群的应用，同时探讨 1-参数子群作用下的转移与不动点概形转移的关系。
摘要：
本文是第一作者与 Gunnar Carlsson 早期工作的延续。我们首先建立的结果之一是动机 Becker-Gottlieb 转移及其艾达尔实现的可加性，这推广了作者已为相应迹建立的可加性结果。随后，我们应用此结果推导出若干重要推论：例如，除获得代数拓扑经典背景下已知的各种双陪集公式的类比外，我们还将其应用于可分闭域上约化群齐次空间的 Brauer 群。我们还考虑了具有 1-参数子群相容作用的概形上的转移与该 1-参数子群不动点概形所关联的转移之间的关系。
英文摘要：
In this paper, which is a continuation of earlier work by the first author and Gunnar Carlsson, one of the first results we establish is the additivity of the motivic Becker-Gottlieb transfer, as well as their étale realizations. This extends the additivity results the authors already established for the corresponding traces. We then apply this to derive several important consequences: for example, in addition to obtaining the analogues of various double coset formulae known in the classical setting of algebraic topology, we also obtain applications to Brauer groups of homogeneous spaces associated to reductive groups over separably closed fields. We also consider the relationship between the transfer on schemes provided with a compatible action by a $1$-parameter subgroup and the transfer associated to the fixed point scheme of the $1$-parameter subgroup.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
