Intersections of Hirzebruch-Zagier divisors and CM cycles / Benjamin Howard, Tonghai Yang
Type de document : MonographieCollection : Lecture notes in mathematics, 2041Langue : anglais.Pays: Allemagne.Éditeur : Berlin : Springer, cop. 2012Description : 1 vol. (VIII-140 p.) ; 24 cmISBN: 9783642239786.ISSN: 0075-8434.Bibliographie : Bibliogr. p. 135-137. Index.Sujet MSC : 11-02, Research exposition (monographs, survey articles) pertaining to number theory11G18, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic aspects of modular and Shimura varieties
11G15, Arithmetic algebraic geometry (Diophantine geometry), Complex multiplication and moduli of abelian varieties
14G40, Arithmetic problems in algebraic geometry. Diophantine geometry, Arithmetic varieties and schemes; Arakelov theory; heightsEn-ligne : Springerlink | Zentralblatt | MathSciNet
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | 11 HOW (Browse shelf(Opens below)) | Available | 12179-01 |
Bibliogr. p. 135-137. Index
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. (Source : Springer)
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