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We study special cycles on a Shimura variety of orthogonal type over atotally real field of degree $d$ associated with a quadratic form in $n+2$variables whose signature is $(n,2)$ at $e$ real places and $(n+2,0)$ at theremaining $d-e$ real places for $1\leq e <d$. Recently, these cycles wereconstructed by Kudla and Rosu-Yott and they proved that the generating seriesof special cycles in the cohomology group is a Hilbert-Siegel modular form ofhalf integral weight. We prove that, assuming the Beilinson-Bloch conjecture onthe injectivity of the higher Abel-Jacobi map, the generating series of specialcycles of codimension $er$ in the Chow group is a Hilbert-Siegel modular formof genus $r$ and weight $1+n/2$. Our result is a generalization of\textit{Kudla's modularity conjecture}, solved by Yuan-Zhang-Zhangunconditionally when $e=1$.

The modularity of special cycles on orthogonal Shimura varieties over totally real fields under the Beilinson-Bloch conjecture