  I employ methods from derived algebraic geometry to give a uniform
moduli-theoretic construction of special cycle classes on integral models many
Shimura varieties of Hodge type, including unitary, quaternionic, and
orthogonal Shimura varieties. All desired properties of these cycles, even for
those corresponding to degenerate Fourier coefficients under the Kudla
correspondence, follow naturally from the construction. I formulate Kudla's
modularity conjectures in this general framework, and give some preliminary
evidence towards their validity.
