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arXiv · 2101.09232

Modularity of special cycles on unitary Shimura varieties over CM-fields

Yota Maeda
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Abstract

We study the modularity of the generating series of special cycles on unitary Shimura varieties over CM-fields of degree $2d$ associated with a Hermitian form in $n+1$ variables whose signature is $(n,1)$ at $e$ real places and $(n+1,0)$ at the remaining $d-e$ real places for $1\leq e 1$, we prove that the generating series of special cycles of codimension $er$ in the Chow group is a Hermitian modular form of weight $n+1$ and genus $r$, assuming the Beilinson-Bloch conjecture with respect to orthogonal Shimura varieties. Our result is a generalization of $\textit{Kudla's modularity conjecture}$, solved by Liu unconditionally when $e=1$.

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Yota Maeda. 2021-01-22. Modularity of special cycles on unitary Shimura varieties over CM-fields. https://doi.org/10.4064/aa210202-12-4

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