虚拟转移因子
Virtual Transfer Factors
摘要：
Langlands-Shelstad转移因子是定义在p-adic域上某些约化群上的函数。在群的原点附近，它可以被看作是李代数上的一个函数。对于典型群，它的值具有形式q^c s，其中s是-1，0或1，q是剩余域的基数，c是有理数。函数s将李代数划分为三个子集。这篇文章表明，这种划分成三个子集是独立的p-adic领域在以下意义。我们定义了三个泛对象（奎因意义下的虚集），使得对于任意具有足够大剩余特征的p-adic域F，这三个虚集的F-点构成划分.算术动机整合理论将一个虚拟周动机与三个虚拟集合中的每一个关联起来。本文中的构造实现了确定控制轨道积分行为的（仍然是抽象的）虚拟Chow动机的长程序的第一步。
英文摘要：
The Langlands-Shelstad transfer factor is a function defined on some reductive groups over a p-adic field. Near the origin of the group, it may be viewed as a function on the Lie algebra. For classical groups, its values have the form q^c s, where s is -1, 0, or 1, q is the cardinality of the residue field, and c is a rational number. The function s partitions the Lie algebra into three subsets. This article shows that this partition into three subsets is independent of the p-adic field in the following sense. We define three universal objects (virtual sets in the sense of Quine) such that for any p-adic field F of sufficiently large residue characteristic, the F-points of these three virtual sets form the partition. The theory of arithmetic motivic integration associates a virtual Chow motive with each of the three virtual sets. The construction in this article achieves the first step in a long program to determine the (still conjectural) virtual Chow motives that control the behavior of orbital integrals.
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