Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds

• Main Author: Weissauer, Rainer. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1968
• Subjects: Mathematics.; Differential equations, partial.; Number theory.; Cell aggregation > Mathematics.; Manifolds and Cell Complexes (incl. Diff.Topology).; Several Complex Variables and Analytic Spaces.; Number Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-89306-6

The geometry of modular curves and the structure of their cohomology groups have been a rich source for various number-theoretical applications over the last decades. Similar applications may be expected from the arithmetic of higher dimensional modular varieties. For Siegel modular threefolds some...

Table of Contents:

• 1 An Application of the Hard Lefschetz Theorem
• 2 CAP-Localization
• 3 The Ramanujan Conjecture for Genus two Siegel modular Forms
• 4 Character Identities and Galois Representations related to the group GSp(4)
• 5 Endoscopy for GSp(4)
• 6 A special Case of the Fundamental Lemma I
• 7 A special Case of the Fundamental Lemma II
• 8 The Langlands-Shelstad transfer factor
• 9 Fundamental lemma (twisted case)
• 10 Reduction to unit elements
• 11 Appendix on Galois cohomology
• 12 Appendix on double cosets.