AI 中文总结
本文推广了Colliot-Thelene的flasque分解理论到任意基上的线性约化群概形，利用Borovoi基本群和Chevalley群自同构的下陷理论构造分解，并应用于环和低维域上的R等价性。
AI 中文摘要
本文研究了任意基上的线性约化群概形的flasque分解，推广了Colliot-Thelene的理论。对于连通基概形（或拟紧、拟分离基概形）上的任何线性约化群概形，都存在flasque分解。该构造依赖于Borovoi基本群以及涉及Chevalley群自同构的下陷理论。应用包括环上及上同调维数至多为2的域上的约化群概形的R等价性。
英文摘要
This paper studies flasque resolutions for linear reductive group schemes over arbitrary bases, extending Colliot-Thelene's theory. A flasque resolution exists for any linear reductive group scheme over a connected base scheme (resp. a quasi-compact, quasi-separated base scheme). The construction relies on Borovoi's fundamental group and descent theory involving automorphisms of Chevalley groups. Applications include R-equivalence for reductive group schemes over rings and over a field of cohomological dimension at most 2.
