Modular Forms and Special Cycles on Shimura Curves. (AM-161) (Annals of Mathematics Studies) - Couverture souple

Kudla, Stephen S.

Couverture souple

ISBN 10 : 0691125511 ISBN 13 : 9780691125510

Editeur : Princeton University Press, 2006

Synopsis

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.

A propos du livre

À propos de l?auteur

Stephen S. Kudla is at the University of Maryland. Michael Rapoport is at the Mathematisches Institut der Universität, Bonn, Germany. Tonghai Yang is at the University of Wisconsin, Madison.

Détails de l'édition

• Éditeur: Princeton University Press
• Date d'édition: 2006
• Langue: anglais
• ISBN 10: 0691125511
• ISBN 13: 9780691125510
• Reliure: Broché
• Nombre de pages: 388
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible