Modularity of special cycles on unitary Shimura varieties over CM-fields

DOI10.4064/aa210202-12-4OpenAlexW3122045421MaRDI QIDQ5093865

Yota Maeda

Publication date: 1 August 2022

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.09232

zbMATH Keywords

algebraic cyclesunitary Shimura varietiesHilbert-Hermitian modular forms

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Arithmetic aspects of modular and Shimura varieties (11G18) Algebraic cycles (14C25)

Related Items (1)

From sum of two squares to arithmetic Siegel–Weil formulas

Cites Work

• Arithmetic theta lifting and \(L\)-derivatives for unitary groups. II
• Algebraic cycles on Shimura varieties of orthogonal type
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• The Gross-Kohnen-Zagier theorem in higher dimensions
• Remarks on generating series for special cycles on orthogonal Shimura varieties
• Borcherds products on unitary groups
• Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables
• Regularized theta lifts for orthogonal groups over totally real fields
• KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES
• The Gross–Kohnen–Zagier theorem over totally real fields
• The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture
• Some cases of Kudla’s modularity conjecture for unitary Shimura varieties

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