Name: Modular Forms and Special Cycles on Shimura Curves (en Inglés)
SKU: 19107172
Price: 1675.35 MXN
Availability: InStock
Author: Kudla, Stephen S. ; Rapoport, Michael ; Yang, Tonghai
ISBN: 9780691125510

portada Modular Forms and Special Cycles on Shimura Curves (en Inglés)

Modular Forms and Special Cycles on Shimura Curves (en Inglés)

Formato

Libro Físico

Autor

Stephen S. Kudla

Michael Rapoport

Tonghai Yang

Editorial

Princeton University Press

Año

2006

Idioma

Inglés

N° páginas

392

Encuadernación

Tapa Blanda

Dimensiones

23.3x15.5x2.6 cm

Peso

0.54 kg.

ISBN

0691125511

ISBN13

9780691125510

Categorías

Análisis funcional y transformaciones
Geometría algebraica

Modular Forms and Special Cycles on Shimura Curves (en Inglés)

Stephen S. Kudla (Autor) · Michael Rapoport (Autor) · Tonghai Yang (Autor) · Princeton University Press · Tapa Blanda

Libro Nuevo Importado

Envío: 13 a 18 días háb.

$ 3,723.01$ 1,675.35

-55%

Costos de importación incluídos en el precio ✅

Libro Nuevo

Quedan más de 100 unidades

$ 1,675.35

¡Envío Gratis! Llega entre el 23 Sep y el 01 Oct a CUAUHTÉMOC, Ciudad de México. Seleccionar ubicación

Agregar a lista de deseos

Reseña del libro "Modular Forms and Special Cycles on Shimura Curves (en Inglés)"

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.