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Automorphic Forms and Shimura Varieties of PGSp(2)

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings.” This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,C) in SL(4, C). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to Langlands’ program in the area of automorphic representations. It includes a proof of known cases of Artin’s conjecture.

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	Science/Engineering Automorphic Forms and Lie Superalgebras
	Science/Engineering Automorphic Forms, Shimura Varieties and L-Functions, Volume 2 Laurent Clozel, “Automorphic Forms, Shimura Varieties and L-Functions, Volume 2” Academic Pr \| 1990-01 \| ISBN: 0121766527 \| 408 pages \| PDF \| 12,6 MB Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held ...
	Science/Engineering Automorphic Forms, Shimura Varieties and L-Functions Laurent Clozel, “Automorphic Forms, Shimura Varieties and L-Functions” Academic Pr \| 1990-01 \| ISBN: 0121766519 \| 456 pages \| PDF \| 20,4 MB Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held at the Un ...
	Science/Engineering Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms Min H. Lee,"Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms"Springer \| June 13, 2008 \| ISBN: 3540219226 \| 239 pages \| PDF \|1.5 mbThis volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domai ...
	Harmonic Analysis, the Trace Formula, and Shimura Varieties Harmonic Analysis, the Trace Formula, and Shimura Varieties Publisher: American Mathematical Society \| ISBN: 082183844X \| edition 2005 \| PDF \| 689 pages \| 4,33 mbThe modern theory of automorphic forms, embodied in what has come to be known ...
	Technical On the Cohomology of Certain Non-Compact Shimura Varieties Sophie Morel, "On the Cohomology of Certain Non-Compact Shimura Varieties" Princeton University Press \| 2010 \| ISBN: 0691142939 \| 256 pages \| PDF \| 1,6 MB This book studies the intersection cohomology of the Shimura varieties associated ...

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	Science/Engineering Automorphic Forms and Lie Superalgebras
	Science/Engineering Automorphic Forms, Shimura Varieties and L-Functions, Volume 2 Laurent Clozel, “Automorphic Forms, Shimura Varieties and L-Functions, Volume 2” Academic Pr \| 1990-01 \| ISBN: 0121766527 \| 408 pages \| PDF \| 12,6 MB Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held ...
	Science/Engineering Automorphic Forms, Shimura Varieties and L-Functions Laurent Clozel, “Automorphic Forms, Shimura Varieties and L-Functions” Academic Pr \| 1990-01 \| ISBN: 0121766519 \| 456 pages \| PDF \| 20,4 MB Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held at the Un ...
	Science/Engineering Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms Min H. Lee,"Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms"Springer \| June 13, 2008 \| ISBN: 3540219226 \| 239 pages \| PDF \|1.5 mbThis volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domai ...
	Harmonic Analysis, the Trace Formula, and Shimura Varieties Harmonic Analysis, the Trace Formula, and Shimura Varieties Publisher: American Mathematical Society \| ISBN: 082183844X \| edition 2005 \| PDF \| 689 pages \| 4,33 mbThe modern theory of automorphic forms, embodied in what has come to be known ...
	Technical On the Cohomology of Certain Non-Compact Shimura Varieties Sophie Morel, "On the Cohomology of Certain Non-Compact Shimura Varieties" Princeton University Press \| 2010 \| ISBN: 0691142939 \| 256 pages \| PDF \| 1,6 MB This book studies the intersection cohomology of the Shimura varieties associated ...

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