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To simplify the inner sum overλ, we set λ′ = r ′(µ′) + m′λ, which yields m′ −1[λ′] = m′ −1[r ′(µ′)] + r ′(µ′)t λ + λt r ′(µ′) + λt m′λ

= X µ′ X t c(f, t) X λ e(t[uλ]τ), where the outer sum runs over µ′ as in the statement, the sum over t ∈ Mat† g (OF )∨ is restricted to t with bottom left block r ′(µ′), the i

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The Geometric Unitary Kudla Conjecture

math.NT · 2026-03-04 · unverdicted · novelty 7.0

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.

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  • The Geometric Unitary Kudla Conjecture math.NT · 2026-03-04 · unverdicted · none · ref 6

    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.