Intersections of Hirzebruch–Zagier Divisors and CM Cycles
Seiten
2012
|
2012
Springer Berlin (Verlag)
978-3-642-23978-6 (ISBN)
Springer Berlin (Verlag)
978-3-642-23978-6 (ISBN)
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.
1. Introduction.- 2. Linear Algebra.- 3. Moduli Spaces of Abelian Surfaces.- 4. Eisenstein Series.- 5. The Main Results.- 6. Local Calculations.
From the reviews:
"The reviewer recommends this beautiful monograph to anyone interested in the circle of conjecture proposed by Kudla et al., particularly from the point of view of arithmetic geometry. The work contains many useful references and intricate proofs that do not appear elsewhere, and is likely to be extremely useful to future progress in the area." (Jeanine Van Order, Zentralblatt MATH, Vol. 1238, 2012)
| Erscheint lt. Verlag | 6.1.2012 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | VIII, 140 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 241 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | 11-XX • Arakelov geometry • Arithmetic intersection theory • automorphic forms • Hilbert modular surfaces |
| ISBN-10 | 3-642-23978-1 / 3642239781 |
| ISBN-13 | 978-3-642-23978-6 / 9783642239786 |
| Zustand | Neuware |
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