Derived special cycles on Shimura varieties

I employ methods from derived algebraic geometry to give a uniform moduli-theoretic construction of special cycle classes on 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. The results apply in particular to classes on GSpin Shimura varieties associated with arbitrary positive semi-definite symmetric matrices, where we recover the classes constructed in work with B. Howard using more classical methods.