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Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds (Paperback, 2009 ed.)
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Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds (Paperback, 2009 ed.)
Series: Lecture Notes in Mathematics, 1968
Expected to ship within 10 - 15 working days
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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.
General
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