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.
Raum where disc(m′) and the theta series are the ones defined in (2.17), and the product on the right hand side is a product of formal series in Ce(τi j)i ,j
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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.