Local Tame Lifting for GL(n) IV: Simple Characters and Base Change
Local Tame Lifting for GL(n) IV: Simple Characters and Base Change
复制标题
GL(n) IV 的局部驯服提升：简单字符和基础更改
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
G. Henniart
中科院分区：
文献类型：
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作者：
C. Bushnell;G. Henniart
设F是一个p进域，K/F是一个有限的、循环的、弱分歧域扩张。在没有任何限制的情况下，我们证明了在亚瑟和Clozel的意义下，从F到K的基变换与作者在早期论文中定义的简单特征标的K/F-提升运算是相容的。这扩展和完成了以前的工作，并代表了一个实质性的一步，以描述tamely分歧基地变化的结构理论的Bushnell和Kutzko表示的目标。我们还给出了朗兰兹对应的一个结果。在证明的主要步骤是表明，提升的简单字符是兼容的自守归纳法，在亨尼亚特和赫伯的意义上，通过一个unramified扩展。这是通过一个新的和独立有趣的结果，关于导体的一对超尖点表示。它给出了一个完整的描述的最小值（一个适当的规范化版本）的导体时，一个表示是固定的。所有关于导体的结果对于正特性的非阿基米德局部场也是有效的。2000年数学学科分类22 E50。
Let F be a p‐adic field and K/F a finite, cyclic, tamely ramified field extension. We show, without any restriction, that base change from F to K, in the sense of Arthur and Clozel, is compatible with the operation of K/F‐lifting for simple characters defined by the authors in an earlier paper. This extends and completes the previous work, and represents a substantial step towards the goal of describing tamely ramified base change in terms of the structure theory of representations of Bushnell and Kutzko. We also give a consequence for the Langlands correspondence. The main step in the proof is to show that lifting of simple characters is compatible with automorphic induction, in the sense of Henniart and Herb, through an unramified extension. This is achieved via a new and independently interesting result concerning the conductor of a pair of supercuspidal representations. It gives a complete description of the minima of (a suitably normalized version of) the conductor when one of the representations is fixed. All results concerning the conductor are also valid for non‐Archimedean local fields of positive characteristic. 2000 Mathematics Subject Classification 22E50.