均匀胞腔剖分及其在Chevalley群上的应用
Uniform cell decomposition with applications to Chevalley groups
摘要：
对非阿基米德局部域，我们统一地表示了可定义函数在可定义集合上的积分，推广了Pas的结果。我们将此应用到Chevalley群，特别是证明了zeta函数计数共轭类的同余式，这样的群体只依赖于大小的剩余域，足够大的剩余特性。特别地，同余商中的共轭类的数目仅取决于剩余域的大小。这同样适用于zeta函数计数维数的Hecke模块的交织运营商相关的诱导表示，这样的子。
英文摘要：
We express integrals of definable functions over definable sets uniformly for non-Archimedean local fields, extending results of Pas. We apply this to Chevalley groups, in particular proving that zeta functions counting conjugacy classes in congruence quotients of such groups depend only on the size of the residue field, for sufficiently large residue characteristic. In particular, the number of conjugacy classes in a congruence quotient depends only on the size of the residue field. The same holds for zeta functions counting dimensions of Hecke modules of intertwining operators associated to induced representations of such quotients.
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