The Geometric Unitary Kudla Conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910206821138432 |
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| author | Raum, Martin |
| author_facet | Raum, Martin |
| contents | We prove that, over an arbitrary CM field, every symmetric formal Fourier-Jacobi series converges and equals the Fourier-Jacobi expansion of a genuine Hermitian Hilbert modular form. As an application, we show that the Chow-valued Kudla generating series of special cycles on unitary Shimura varieties for Hermitian lattices over CM fields of signature $(p,1)$ at one infinite place and $(p+1,0)$ at all others is modular of weight $p+1$ for a Weil representation, establishing the geometric unitary Kudla Conjecture in arbitrary codimension. This removes the modularity hypothesis from the arithmetic inner product formula by Li-Liu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04282 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Geometric Unitary Kudla Conjecture Raum, Martin Number Theory We prove that, over an arbitrary CM field, every symmetric formal Fourier-Jacobi series converges and equals the Fourier-Jacobi expansion of a genuine Hermitian Hilbert modular form. As an application, we show that the Chow-valued Kudla generating series of special cycles on unitary Shimura varieties for Hermitian lattices over CM fields of signature $(p,1)$ at one infinite place and $(p+1,0)$ at all others is modular of weight $p+1$ for a Weil representation, establishing the geometric unitary Kudla Conjecture in arbitrary codimension. This removes the modularity hypothesis from the arithmetic inner product formula by Li-Liu. |
| title | The Geometric Unitary Kudla Conjecture |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.04282 |