Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds
Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds
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DOI：
10.1007/978-3-540-89306-6
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发表时间：
2009-03
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通讯作者：
R. Weissauer
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作者：
R. Weissauer
这卷书是从1993年到1994年之间编写和发行的一系列预印本中发展出来的。大约在同一时间，哈德[40]和劳蒙[62]独立完成了相关工作。在写这篇文章的基础上，这些预印本，在1995年夏天广泛分发的修订版，我？nally并没有放弃最初的计划，完全重组原来的预印本。在长时间的延迟之后，其中一个原因是现在可以在[115]中获得结果的概述。相反，我试图适度地改进演示文稿，特别是在我认为有必要的地方添加交叉引用。此外，Chaps。11和12和教派。5.一五4和5中所示。其中5个是在1998年写的。我会给一个更详细的概述的内容不同的章节下面。在此之前，我应该提到的两个主要结果是证明拉马努金猜想西格尔模形式的亏格2的形式，这不是尖表示与抛物子群（CAP表示），和研究的内窥镜升降机组GSp（4）。这两个主题的制定和证明？rst？五章假定迹公式稳定。所有其余的技术成果，这是必要的，以获得稳定的轨迹公式，在其余章节。第1章收集的结果上同调西格尔模三倍，在后面的章节中使用，特别是在第一章。3.在第一章开始。
This volume grew out of a series of preprints which were written and circulated-tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I? nally did not p-sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now available in [115]. Instead I tried to improve the presentation modestly, in particular by adding cross-references wherever I felt this was necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5 were added; these were written in 1998. I willgivea moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that I should mention that the two main results are the proof of Ramanujan’s conjecture for Siegel modular forms of genus 2 for forms which are not cuspidal representations associated with parabolic subgroups (CAP representations), and the study of the endoscopic lift for the group GSp (4). Both topics are formulated and proved in the? rst? ve chapters assuming the stabilization of the trace formula. All the remaining technical results, which are necessary to obtain the stabilized trace formula, are presented in the remaining chapters. Chapter 1 gathers results on the cohomology of Siegel modular threefolds that are used in later chapters, notably in Chap. 3. At the beginning of Chap.