Some cases of Kudla’s modularity conjecture for unitary Shimura varieties
Copyright policy )Some cases of Kudla’s modularity conjecture for unitary Shimura varieties
Abstract We use the method of Bruinier–Raum to show that symmetric formal Fourier–Jacobi series, in the cases of norm-Euclidean imaginary quadratic fields, are Hermitian modular forms. Consequently, combining a theorem of Yifeng Liu, we deduce Kudla’s conjecture on the modularity of generating series of special cycles of arbitrary codimension for unitary Shimura varieties defined in these cases.
- Université Laval Canada
11G18, 11F27, 14G35, Mathematics - Number Theory, unitary Shimura varieties, Modular and Shimura varieties, Mathematics - Algebraic Geometry, theta series, special cycles, generating functions, Jacobi forms, FOS: Mathematics, Theta series; Weil representation; theta correspondences, Kudla's modularity conjecture, Number Theory (math.NT), Arithmetic aspects of modular and Shimura varieties, Algebraic Geometry (math.AG)
11G18, 11F27, 14G35, Mathematics - Number Theory, unitary Shimura varieties, Modular and Shimura varieties, Mathematics - Algebraic Geometry, theta series, special cycles, generating functions, Jacobi forms, FOS: Mathematics, Theta series; Weil representation; theta correspondences, Kudla's modularity conjecture, Number Theory (math.NT), Arithmetic aspects of modular and Shimura varieties, Algebraic Geometry (math.AG)
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