Intersections of Hirzebruch?Zagier - E-book

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Intersections Of Hirzebruch?zagier Divisors And Cm Cycles - ENG

Benjamin Howard; Tonghai Yang

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Sinopsis

ISBN:	9783642239793
Formato:	Page Fidelity
Idioma:	Inglés
Editorial:	Springer Nature
Tema:	Matemáticas
Subtema:	Teoría dos Números
Año de publicación:	2012-01-05

This monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert modular surface, and the special cycles are complex multiplication points and the Hirzebruch-Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.

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