Automorphic Forms and Shimura Varieties of PGSp(2) (Hardback)
  • Automorphic Forms and Shimura Varieties of PGSp(2) (Hardback)

Automorphic Forms and Shimura Varieties of PGSp(2) (Hardback)

Hardback Published: 15/08/2005
  • Can be ordered from our supplier

Delivered within 2 weeks

  • This item has been added to your basket

Check Marketplace availability

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,<=) in SL(4, <=). 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.

Publisher: World Scientific Publishing Co Pte Ltd
ISBN: 9789812564030

You may also be interested in...

Your review has been submitted successfully.

We would love to hear what you think of Waterstones. Why not review Waterstones on Trustpilot?

Review us on Trustpilot