Some cases of Kudla’s modularity conjecture for unitary Shimura varieties

DOI10.1017/fms.2022.26zbMath1500.11051arXiv2101.06304OpenAlexW4298308181WikidataQ113858336 ScholiaQ113858336MaRDI QIDQ5866300

Jiacheng Xia

Publication date: 13 June 2022

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.06304

zbMATH Keywords

generating functionsJacobi formstheta seriesspecial cyclesunitary Shimura varietiesKudla's modularity conjecture

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items

Modularity of special cycles on unitary Shimura varieties over CM-fields, From sum of two squares to arithmetic Siegel–Weil formulas

Cites Work

• Arithmetic theta lifting and \(L\)-derivatives for unitary groups. I
• Modular descent and the Saito-Kurokawa conjecture
• Algebraic cycles on Shimura varieties of orthogonal type
• The theory of Jacobi forms
• Jacobi forms of higher degree
• The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004
• The theta correspondence and harmonic forms. I
• The theta correspondence and harmonic forms. II
• Heegner points and derivatives of \(L\)-series. II
• Automorphic forms with singularities on Grassmannians
• Toroidal compactification of Siegel spaces
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Über eine Spezialschar von Modulformen zweiten Grades. (On a Spezialschar of modular forms of second degree.)
• On certain reciprocity-laws for theta functions and modular forms
• Über eine Spezialschar von Modulformen zweiten Grades. II, III. (On a Spezialschar of modular forms of second degree. II, III)
• Multiplier systems and characters for Hermitian modular groups
• Central extensions of simply connected algebraic groups and Galois cohomology
• Computation of the metaplectic kernel
• Deligne's topological central extension is universal.
• Vector-valued modular forms and Poincaré series
• Central extensions of reductive groups by \(K_2\).
• Hermitian Jacobi forms
• Jacobi forms that characterize paramodular forms
• 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
• Hermitian modular functions
• Hermitian modular functions. II: Genus invariants of Hermitian forms
• Hermitian modular functions. III. The hermitian modular group
• Formal Fourier Jacobi expansions and special cycles of codimension two
• On the Fourier–Jacobi expansion of the unitary Kudla lift
• KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES
• Contributions from Conjugacy Classes of Regular Elliptic Elements in Hermitian Modular Groups to the Dimension Formula of Hermitian Modular Cusp Forms
• L-functions attached to Jacobi forms of degree n. Part I. The basic identity.
• Stable real cohomology of arithmetic groups
• A Dimension Formula for Hermitian Modular Cusp Forms of Degree Two
• Arithmetic divisors on orthogonal and unitary Shimura varieties
• Vector valued formal Fourier-Jacobi series
• The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item