Field Patching, Factorization, and Local–Global Principles
Field Patching, Factorization, and Local–Global Principles
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现场修补、分解和局部-全局原则
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发表时间：
2009
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通讯作者：
D. Krashen
中科院分区：
文献类型：
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作者：
D. Krashen
域拼接方法在伽罗瓦理论、中心单代数和二次型上的结果已被证明是有用的。其中的一个关键因素是证明了连通有理线性代数群的某些“因式分解”结果。本文通过考察因式分解结果与局部-全局原理之间的关系，以及将已知的因式分解结果推广到连通的、收缩的有理线性代数群，来探索域修补的其他可能的应用。
The method of field patching has proven useful in obtaining results on Galois theory, central simple algebras, and quadratic forms. A crucial ingredient for this was proving certain “factorization” results for connected, rational linear algebraic groups. In this paper, we explore other possible applications of field patching by examining the relationship between factorization results and local–global principles, and also by extending the known factorization results to connected, retract rational linear algebraic groups.