Derived cycles on Shimura varieties

I will show how methods from derived algebraic geometry can be used to give a uniform definition of generating series of cycles on integral models of Shimura varieties of Hodge or even abelian type. Following conjectures of Kudla, these series are expected to converge to half-integer weight automorphic forms on split unitary groups, and certain ‘easy’ consequences of this expectation turn out to be indeed easy given the derived perspective.