Over CM fields, symmetric formal Fourier-Jacobi series converge to genuine Hermitian Hilbert modular forms, proving the geometric unitary Kudla conjecture for Chow-valued Kudla generating series of special cycles on unitary Shimura varieties in arbitrary codimension.
4.3 The final convergence statement We are now in a position to prove Theorem C, which is a synthesis of Theorem 3.15 with Proposition 4.3 and Proposition 4.5
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The Geometric Unitary Kudla Conjecture
Over CM fields, symmetric formal Fourier-Jacobi series converge to genuine Hermitian Hilbert modular forms, proving the geometric unitary Kudla conjecture for Chow-valued Kudla generating series of special cycles on unitary Shimura varieties in arbitrary codimension.