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Titlebook: Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds; Rainer Weissauer Book 2009 Springer-Verlag Berlin Heidelberg 2009 Ra

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书目名称Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds
编辑Rainer Weissauer
视频video
概述Includes supplementary material:
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds;  Rainer Weissauer Book 2009 Springer-Verlag Berlin Heidelberg 2009 Ra
描述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
出版日期Book 2009
关键词Ramanujan‘s conjecture; Selberg trace formula; automorphic representations; cohomology; cohomology group
版次1
doihttps://doi.org/10.1007/978-3-540-89306-6
isbn_softcover978-3-540-89305-9
isbn_ebook978-3-540-89306-6Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2009
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Local and Global Endoscopy for GSp(4), 5.2, which is a special case of a global multiplicity formula conjectured by Arthur.We consider the symplectic group .(4) over an arbitrary totally real number field .. In the special case . = Q and for irreducible automorphic representations π with π. in the discrete series the proof of this theor
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Fundamental lemma (twisted case),wisted base change endoscopy. In fact, this is shown in this chapter for the unit elements of the Hecke algebras.Using global arguments involving the Selberg trace formula, it suffices to prove the fundamental lemma and twisted fundamental lemma in general assuming the fundamental lemma for unit ele
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Reduction to unit elements, case of twisted endoscopy, although formulated only for .′ = .(4) and base change in this chapter, holds for twisted endoscopy in greater generality. However, to avoid technical considerations, we restrict ourselves here to the special case. The general case will be considered elsewhere [113].
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