The Gross–Kohnen–Zagier theorem over totally real fields

DOI10.1112/S0010437X08003734zbMath1235.11056MaRDI QIDQ3642510

Wei Zhang, Xinyi Yuan, Shou-Wu Zhang

Publication date: 5 November 2009

Published in: Compositio Mathematica (Search for Journal in Brave)

zbMATH Keywords

Shimura varietiesSiegel modular formsspecial cyclesKudla cycles

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items (13)

KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES ⋮ Modularity of special cycles on unitary Shimura varieties over CM-fields ⋮ From sum of two squares to arithmetic Siegel–Weil formulas ⋮ The -adic Gross–Zagier formula on Shimura curves ⋮ Generating series of a new class of orthogonal Shimura varieties ⋮ Arithmetic theta lifts and the arithmetic Gan-Gross-Prasad conjecture for unitary groups ⋮ Weil representation and arithmetic fundamental lemma ⋮ Mixed Arithmetic Theta Lifting for Unitary Groups ⋮ Chow groups and \(L\)-derivatives of automorphic motives for unitary groups ⋮ The \(p\)-adic variation of the Gross-Kohnen-Zagier theorem ⋮ Remarks on generating series for special cycles on orthogonal Shimura varieties ⋮ The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture ⋮ Regularized theta lifts for orthogonal groups over totally real fields

Cites Work

• Algebraic cycles on Shimura varieties of orthogonal type
• Gross-Zagier formula for \(\text{GL}_ 2\).
• Heegner points and derivatives of \(L\)-series
• Heegner points and derivatives of \(L\)-series. II
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• The Gross-Kohnen-Zagier theorem in higher dimensions
• Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables

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